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Robust stochastic optimization with convex risk measures: A discretized subgradient scheme
A diagonal PRP-type projection method for convex constrained nonlinear monotone equations
Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, 700241, Nigeria |
Iterative methods for nonlinear monotone equations do not require the differentiability assumption on the residual function. This special property of the methods makes them suitable for solving large-scale nonsmooth monotone equations. In this work, we present a diagonal Polak-Ribi$ \grave{e} $re-Polyak (PRP) conjugate gradient-type method for solving large-scale nonlinear monotone equations with convex constraints. The search direction is a combine form of a multivariate (diagonal) spectral method and a modified PRP conjugate gradient method. Proper safeguards are devised to ensure positive definiteness of the diagonal matrix associated with the search direction. Based on Lipschitz continuity and monotonicity assumptions the method is shown to be globally convergent. Numerical results are presented by means of comparative experiments with recently proposed multivariate spectral Dai-Yuan-type (J. Ind. Manag. Optim. 13 (2017) 283-295) and Wei-Yao-Liu-type (Int. J. Comput. Math. 92 (2015) 2261-2272) conjugate gradient methods.
References:
[1] |
A. B. Abubakar and P. Kumam,
An improved three-term derivative-free method for solving nonlinear equations, Comput. Appl. Math., 37 (2018), 6760-6773.
doi: 10.1007/s40314-018-0712-5. |
[2] |
A. B. Abubakar and P. Kumam,
A descent Dai-Liao conjugate gradient method for nonlinear equations, Numer. Algorithms, 81 (2019), 197-210.
doi: 10.1007/s11075-018-0541-z. |
[3] |
Y. Bing and G. Lin,
An efficient implementation of Merrill's method for sparse or partially separable systems of nonlinear equations, SIAM J. Optim., 1 (1991), 206-221.
doi: 10.1137/0801015. |
[4] |
W. Cheng,
A PRP type method for systems of monotone equations, Math. Comput. Modelling, 50 (2009), 15-20.
doi: 10.1016/j.mcm.2009.04.007. |
[5] |
Y. Dai and Y. Yuan,
A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), 177-182.
doi: 10.1137/S1052623497318992. |
[6] |
E. D. Dolan and J. J. Moré,
Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[7] |
X. L. Dong, H. Liu, Y. L. Xu and X. M. Yang,
Some nonlinear conjugate gradient methods with sufficient descent condition and global convergence, Optim. Lett., 9 (2015), 1421-1432.
doi: 10.1007/s11590-014-0836-5. |
[8] |
M. Eshaghnezhad, S. Effati and A. Mansoori,
A neurodynamic model to solve nonlinear pseudo-monotone projection equation and its applications, IEEE Transactions on Cybernetics, 47 (2017), 3050-3062.
doi: 10.1109/TCYB.2016.2611529. |
[9] |
M. Fukushima,
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[10] |
B. Ghaddar, J. Marecek and M. Mevissen,
Optimal power flow as a polynomial optimization problem, IEEE Transactions on Power Systems, 31 (2016), 539-546.
doi: 10.1109/TPWRS.2015.2390037. |
[11] |
B. Gu, V. S. Sheng, K. Y. Tay, W. Romano and S. Li,
Incremental support vector learning for ordinal regression, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 1403-1416.
doi: 10.1109/TNNLS.2014.2342533. |
[12] |
L. Han, G. Yu and L. Guan,
Multivariate spectral gradient method for unconstrained optimization, Appl. Math. Comput., 201 (2008), 621-630.
doi: 10.1016/j.amc.2007.12.054. |
[13] |
Y. Hu and Z. Wei,
Wei–Yao–Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints, Int. J. Comput. Math., 92 (2015), 2261-2272.
doi: 10.1080/00207160.2014.977879. |
[14] |
W. La Cruz,
A projected derivative-free algorithm for nonlinear equations with convex constraints, Optim. Methods Softw., 29 (2014), 24-41.
doi: 10.1080/10556788.2012.721129. |
[15] |
W. La Cruz,
A spectral algorithm for large-scale systems of nonlinear monotone equations, Numer. Algorithms, 76 (2017), 1109-1130.
doi: 10.1007/s11075-017-0299-8. |
[16] |
W. La Cruz, J. Martínez and M. Raydan,
Spectral residual method without gradient information for solving large-scale nonlinear systems of equations, Math. Comp., 75 (2006), 1429-1448.
doi: 10.1090/S0025-5718-06-01840-0. |
[17] |
J. Li, X. Li, B. Yang and X. Sun, Segmentation-based image copy-move forgery detection scheme, IEEE Transactions on Information Forensics and Security, 10 (2015), 507-518. Google Scholar |
[18] |
Q. Li and D. H. Li,
A class of derivative-free methods for large-scale nonlinear monotone equations, IMA J. Numer. Anal., 31 (2011), 1625-1635.
doi: 10.1093/imanum/drq015. |
[19] |
J. Liu and X. L. Du,
A gradient projection method for the sparse signal reconstruction in compressive sensing, Appl. Anal., 97 (2018), 2122-2131.
doi: 10.1080/00036811.2017.1359556. |
[20] |
J. Liu and Y. Duan, Two spectral gradient projection methods for constrained equations and their linear convergence rate, J. Inequal. Appl., 2015 (2015), 13pp.
doi: 10.1186/s13660-014-0525-z. |
[21] |
J. Liu and Y. Feng,
A derivative-free iterative method for nonlinear monotone equations with convex constraints, Numerical Algorithms, 82 (2019), 1-18.
doi: 10.1007/s11075-018-0603-2. |
[22] |
J. Liu and S. Li,
Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations, J. Ind. Manag. Optim., 13 (2017), 283-295.
doi: 10.3934/jimo.2016017. |
[23] |
J. Liu and S. Li,
A projection method for convex constrained monotone nonlinear equations with applications, Comput. Math. Appl., 70 (2015), 2442-2453.
doi: 10.1016/j.camwa.2015.09.014. |
[24] |
S. Liu, Y. Huang and H. W. Jiao, Sufficient descent conjugate gradient methods for solving convex constrained nonlinear monotone equations, Abstr. Appl. Anal., 2014 (2014), 12pp.
doi: 10.1155/2014/305643. |
[25] |
F. Ma and C. Wang,
Modified projection method for solving a system of monotone equations with convex constraints, J. Appl. Math. Comput., 34 (2010), 47-56.
doi: 10.1007/s12190-009-0305-y. |
[26] |
H. Mohammad and A. B. Abubakar,
A positive spectral gradient-like method for nonlinear monotone equations, Bull. Comput. Appl. Math., 5 (2017), 99-115.
|
[27] |
H. Mohammad and S. A. Santos,
A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares, Comput. Appl. Math., 37 (2018), 6619-6653.
doi: 10.1007/s40314-018-0696-1. |
[28] |
Y. Ou and J. Li,
A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints, J. Appl. Math. Comput., 56 (2018), 195-216.
doi: 10.1007/s12190-016-1068-x. |
[29] |
Y. Ou and Y. Liu,
Supermemory gradient methods for monotone nonlinear equations with convex constraints, Comput. Appl. Math., 36 (2017), 259-279.
doi: 10.1007/s40314-015-0228-1. |
[30] |
Z. Papp and S. Rapajić,
FR type methods for systems of large-scale nonlinear monotone equations, Appl. Math. Comput., 269 (2015), 816-823.
doi: 10.1016/j.amc.2015.08.002. |
[31] |
E. Polak and G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Revue française d'informatique et de recherche opérationnelle. Série rouge, 3 (1969), 35–43. |
[32] |
B. T. Polyak,
The conjugate gradient method in extremal problems, USSR Comp. Math. and Mathem. Physics, 9 (1969), 94-112.
doi: 10.1016/0041-5553(69)90035-4. |
[33] |
G. Qian, D. Han, L. Xu and H. Y.,
Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities, J. Ind. Manag. Optim., 9 (2013), 255-274.
doi: 10.3934/jimo.2013.9.255. |
[34] |
M. V. Solodov and B. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Applied Optimization, Springer, 1998,355–369.
doi: 10.1007/978-1-4757-6388-1_18. |
[35] |
M. Sun and J. Liu,
Three derivative-free projection methods for nonlinear equations with convex constraints, J. Appl. Math. Comput., 47 (2015), 265-276.
doi: 10.1007/s12190-014-0774-5. |
[36] |
C. Wang and Y. Wang,
A superlinearly convergent projection method for constrained systems of nonlinear equations, J. Global Optim., 44 (2009), 283-296.
doi: 10.1007/s10898-008-9324-8. |
[37] |
C. Wang, Y. Wang and C. Xu,
A projection method for a system of nonlinear monotone equations with convex constraints, Math. Methods Oper. Res., 66 (2007), 33-46.
doi: 10.1007/s00186-006-0140-y. |
[38] |
X. Wang, S. Li and X. Kou,
A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints, Calcolo, 53 (2016), 133-145.
doi: 10.1007/s10092-015-0140-5. |
[39] |
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, John Wiley & Sons, 2012. Google Scholar |
[40] |
Y. Xiao and H. Zhu,
A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing, J. Math. Anal. Appl., 405 (2013), 310-319.
doi: 10.1016/j.jmaa.2013.04.017. |
[41] |
Q. Yan, X. Z. Peng and D. H. Li,
A globally convergent derivative-free method for solving large-scale nonlinear monotone equations, J. Comput. Appl. Math., 234 (2010), 649-657.
doi: 10.1016/j.cam.2010.01.001. |
[42] |
G. Yu, S. Niu and J. Ma,
Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints, J. Ind. Manag. Optim., 9 (2013), 117-129.
doi: 10.3934/jimo.2013.9.117. |
[43] |
Z. Yu, J. Lin, J. Sun, Y. H. Xiao, L. Liu and Z. H. Li,
Spectral gradient projection method for monotone nonlinear equations with convex constraints, Appl. Numer. Math., 59 (2009), 2416-2423.
doi: 10.1016/j.apnum.2009.04.004. |
[44] |
N. Yuan,
A derivative-free projection method for solving convex constrained monotone equations, SCIENCEASIA, 43 (2017), 195-200.
doi: 10.2306/scienceasia1513-1874.2017.43.195. |
[45] |
M. Zhang, Y. Xiao and H. Dou,
Solving nonlinear constrained monotone equations via limited memory BFGS algorithm, J. of Comp. Infor. Syst., 7 (2011), 3995-4006.
|
[46] |
Y. Zheng, B. Jeon, D. Xu, Q. M. Wu and H. Zhang, Image segmentation by generalized hierarchical fuzzy c-means algorithm, J. of Int. & Fuzzy Syst., 28 (2015), 961-973. Google Scholar |
[47] |
W. Zhou and D. H. Li,
Limited memory BFGS method for nonlinear monotone equations, J. Comput. Math., 25 (2007), 89-96.
|
[48] |
W. Zhou and F. Wang,
A PRP-based residual method for large-scale monotone nonlinear equations, Appl. Math. Comput., 261 (2015), 1-7.
doi: 10.1016/j.amc.2015.03.069. |
show all references
References:
[1] |
A. B. Abubakar and P. Kumam,
An improved three-term derivative-free method for solving nonlinear equations, Comput. Appl. Math., 37 (2018), 6760-6773.
doi: 10.1007/s40314-018-0712-5. |
[2] |
A. B. Abubakar and P. Kumam,
A descent Dai-Liao conjugate gradient method for nonlinear equations, Numer. Algorithms, 81 (2019), 197-210.
doi: 10.1007/s11075-018-0541-z. |
[3] |
Y. Bing and G. Lin,
An efficient implementation of Merrill's method for sparse or partially separable systems of nonlinear equations, SIAM J. Optim., 1 (1991), 206-221.
doi: 10.1137/0801015. |
[4] |
W. Cheng,
A PRP type method for systems of monotone equations, Math. Comput. Modelling, 50 (2009), 15-20.
doi: 10.1016/j.mcm.2009.04.007. |
[5] |
Y. Dai and Y. Yuan,
A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), 177-182.
doi: 10.1137/S1052623497318992. |
[6] |
E. D. Dolan and J. J. Moré,
Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[7] |
X. L. Dong, H. Liu, Y. L. Xu and X. M. Yang,
Some nonlinear conjugate gradient methods with sufficient descent condition and global convergence, Optim. Lett., 9 (2015), 1421-1432.
doi: 10.1007/s11590-014-0836-5. |
[8] |
M. Eshaghnezhad, S. Effati and A. Mansoori,
A neurodynamic model to solve nonlinear pseudo-monotone projection equation and its applications, IEEE Transactions on Cybernetics, 47 (2017), 3050-3062.
doi: 10.1109/TCYB.2016.2611529. |
[9] |
M. Fukushima,
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[10] |
B. Ghaddar, J. Marecek and M. Mevissen,
Optimal power flow as a polynomial optimization problem, IEEE Transactions on Power Systems, 31 (2016), 539-546.
doi: 10.1109/TPWRS.2015.2390037. |
[11] |
B. Gu, V. S. Sheng, K. Y. Tay, W. Romano and S. Li,
Incremental support vector learning for ordinal regression, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 1403-1416.
doi: 10.1109/TNNLS.2014.2342533. |
[12] |
L. Han, G. Yu and L. Guan,
Multivariate spectral gradient method for unconstrained optimization, Appl. Math. Comput., 201 (2008), 621-630.
doi: 10.1016/j.amc.2007.12.054. |
[13] |
Y. Hu and Z. Wei,
Wei–Yao–Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints, Int. J. Comput. Math., 92 (2015), 2261-2272.
doi: 10.1080/00207160.2014.977879. |
[14] |
W. La Cruz,
A projected derivative-free algorithm for nonlinear equations with convex constraints, Optim. Methods Softw., 29 (2014), 24-41.
doi: 10.1080/10556788.2012.721129. |
[15] |
W. La Cruz,
A spectral algorithm for large-scale systems of nonlinear monotone equations, Numer. Algorithms, 76 (2017), 1109-1130.
doi: 10.1007/s11075-017-0299-8. |
[16] |
W. La Cruz, J. Martínez and M. Raydan,
Spectral residual method without gradient information for solving large-scale nonlinear systems of equations, Math. Comp., 75 (2006), 1429-1448.
doi: 10.1090/S0025-5718-06-01840-0. |
[17] |
J. Li, X. Li, B. Yang and X. Sun, Segmentation-based image copy-move forgery detection scheme, IEEE Transactions on Information Forensics and Security, 10 (2015), 507-518. Google Scholar |
[18] |
Q. Li and D. H. Li,
A class of derivative-free methods for large-scale nonlinear monotone equations, IMA J. Numer. Anal., 31 (2011), 1625-1635.
doi: 10.1093/imanum/drq015. |
[19] |
J. Liu and X. L. Du,
A gradient projection method for the sparse signal reconstruction in compressive sensing, Appl. Anal., 97 (2018), 2122-2131.
doi: 10.1080/00036811.2017.1359556. |
[20] |
J. Liu and Y. Duan, Two spectral gradient projection methods for constrained equations and their linear convergence rate, J. Inequal. Appl., 2015 (2015), 13pp.
doi: 10.1186/s13660-014-0525-z. |
[21] |
J. Liu and Y. Feng,
A derivative-free iterative method for nonlinear monotone equations with convex constraints, Numerical Algorithms, 82 (2019), 1-18.
doi: 10.1007/s11075-018-0603-2. |
[22] |
J. Liu and S. Li,
Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations, J. Ind. Manag. Optim., 13 (2017), 283-295.
doi: 10.3934/jimo.2016017. |
[23] |
J. Liu and S. Li,
A projection method for convex constrained monotone nonlinear equations with applications, Comput. Math. Appl., 70 (2015), 2442-2453.
doi: 10.1016/j.camwa.2015.09.014. |
[24] |
S. Liu, Y. Huang and H. W. Jiao, Sufficient descent conjugate gradient methods for solving convex constrained nonlinear monotone equations, Abstr. Appl. Anal., 2014 (2014), 12pp.
doi: 10.1155/2014/305643. |
[25] |
F. Ma and C. Wang,
Modified projection method for solving a system of monotone equations with convex constraints, J. Appl. Math. Comput., 34 (2010), 47-56.
doi: 10.1007/s12190-009-0305-y. |
[26] |
H. Mohammad and A. B. Abubakar,
A positive spectral gradient-like method for nonlinear monotone equations, Bull. Comput. Appl. Math., 5 (2017), 99-115.
|
[27] |
H. Mohammad and S. A. Santos,
A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares, Comput. Appl. Math., 37 (2018), 6619-6653.
doi: 10.1007/s40314-018-0696-1. |
[28] |
Y. Ou and J. Li,
A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints, J. Appl. Math. Comput., 56 (2018), 195-216.
doi: 10.1007/s12190-016-1068-x. |
[29] |
Y. Ou and Y. Liu,
Supermemory gradient methods for monotone nonlinear equations with convex constraints, Comput. Appl. Math., 36 (2017), 259-279.
doi: 10.1007/s40314-015-0228-1. |
[30] |
Z. Papp and S. Rapajić,
FR type methods for systems of large-scale nonlinear monotone equations, Appl. Math. Comput., 269 (2015), 816-823.
doi: 10.1016/j.amc.2015.08.002. |
[31] |
E. Polak and G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Revue française d'informatique et de recherche opérationnelle. Série rouge, 3 (1969), 35–43. |
[32] |
B. T. Polyak,
The conjugate gradient method in extremal problems, USSR Comp. Math. and Mathem. Physics, 9 (1969), 94-112.
doi: 10.1016/0041-5553(69)90035-4. |
[33] |
G. Qian, D. Han, L. Xu and H. Y.,
Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities, J. Ind. Manag. Optim., 9 (2013), 255-274.
doi: 10.3934/jimo.2013.9.255. |
[34] |
M. V. Solodov and B. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Applied Optimization, Springer, 1998,355–369.
doi: 10.1007/978-1-4757-6388-1_18. |
[35] |
M. Sun and J. Liu,
Three derivative-free projection methods for nonlinear equations with convex constraints, J. Appl. Math. Comput., 47 (2015), 265-276.
doi: 10.1007/s12190-014-0774-5. |
[36] |
C. Wang and Y. Wang,
A superlinearly convergent projection method for constrained systems of nonlinear equations, J. Global Optim., 44 (2009), 283-296.
doi: 10.1007/s10898-008-9324-8. |
[37] |
C. Wang, Y. Wang and C. Xu,
A projection method for a system of nonlinear monotone equations with convex constraints, Math. Methods Oper. Res., 66 (2007), 33-46.
doi: 10.1007/s00186-006-0140-y. |
[38] |
X. Wang, S. Li and X. Kou,
A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints, Calcolo, 53 (2016), 133-145.
doi: 10.1007/s10092-015-0140-5. |
[39] |
A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, John Wiley & Sons, 2012. Google Scholar |
[40] |
Y. Xiao and H. Zhu,
A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing, J. Math. Anal. Appl., 405 (2013), 310-319.
doi: 10.1016/j.jmaa.2013.04.017. |
[41] |
Q. Yan, X. Z. Peng and D. H. Li,
A globally convergent derivative-free method for solving large-scale nonlinear monotone equations, J. Comput. Appl. Math., 234 (2010), 649-657.
doi: 10.1016/j.cam.2010.01.001. |
[42] |
G. Yu, S. Niu and J. Ma,
Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints, J. Ind. Manag. Optim., 9 (2013), 117-129.
doi: 10.3934/jimo.2013.9.117. |
[43] |
Z. Yu, J. Lin, J. Sun, Y. H. Xiao, L. Liu and Z. H. Li,
Spectral gradient projection method for monotone nonlinear equations with convex constraints, Appl. Numer. Math., 59 (2009), 2416-2423.
doi: 10.1016/j.apnum.2009.04.004. |
[44] |
N. Yuan,
A derivative-free projection method for solving convex constrained monotone equations, SCIENCEASIA, 43 (2017), 195-200.
doi: 10.2306/scienceasia1513-1874.2017.43.195. |
[45] |
M. Zhang, Y. Xiao and H. Dou,
Solving nonlinear constrained monotone equations via limited memory BFGS algorithm, J. of Comp. Infor. Syst., 7 (2011), 3995-4006.
|
[46] |
Y. Zheng, B. Jeon, D. Xu, Q. M. Wu and H. Zhang, Image segmentation by generalized hierarchical fuzzy c-means algorithm, J. of Int. & Fuzzy Syst., 28 (2015), 961-973. Google Scholar |
[47] |
W. Zhou and D. H. Li,
Limited memory BFGS method for nonlinear monotone equations, J. Comput. Math., 25 (2007), 89-96.
|
[48] |
W. Zhou and F. Wang,
A PRP-based residual method for large-scale monotone nonlinear equations, Appl. Math. Comput., 261 (2015), 1-7.
doi: 10.1016/j.amc.2015.03.069. |



INITIAL POINT | VALUE |
|
|
INITIAL POINT | VALUE |
|
|
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 5 | 14 | 0.2355 | 8.79E-08 | 16 | 69 | 0.0200 | 4.84E-06 | 2 | 9 | 0.0085 | 0.00E+00 | |
4 | 11 | 0.0156 | 1.06E-08 | 10 | 40 | 0.0126 | 5.44E-06 | 4 | 15 | 0.0079 | 0.00E+00 | ||
15 | 35 | 0.0887 | 6.01E-06 | 13 | 54 | 0.1723 | 7.55E-06 | 5 | 20 | 0.0119 | 0.00E+00 | ||
6 | 16 | 0.0204 | 5.47E-06 | 25 | 133 | 0.1284 | 3.35E-06 | 2 | 9 | 0.0079 | 0.00E+00 | ||
8 | 20 | 0.0294 | 2.47E-06 | 27 | 138 | 0.0757 | 6.03E-06 | 2 | 11 | 0.0076 | 0.00E+00 | ||
8 | 19 | 0.0362 | 1.95E-06 | 26 | 134 | 0.0350 | 4.52E-06 | 4 | 15 | 0.0102 | 0.00E+00 | ||
8 | 20 | 0.0292 | 2.48E-06 | 25 | 133 | 0.1248 | 3.35E-06 | 2 | 11 | 0.0071 | 0.00E+00 | ||
8 | 20 | 0.0299 | 2.49E-06 | 22 | 112 | 0.0317 | 4.53E-06 | 2 | 11 | 0.0080 | 0.00E+00 | ||
5 | 14 | 0.0720 | 1.71E-07 | 17 | 73 | 0.0820 | 2.67E-06 | 2 | 9 | 0.0143 | 0.00E+00 | ||
4 | 11 | 0.0457 | 2.31E-08 | 8 | 31 | 0.0563 | 8.85E-06 | 4 | 15 | 0.0182 | 0.00E+00 | ||
15 | 35 | 0.0707 | 6.05E-06 | 13 | 54 | 1.5146 | 7.55E-06 | 5 | 20 | 0.0308 | 0.00E+00 | ||
6 | 16 | 0.0492 | 5.61E-06 | 24 | 126 | 0.1178 | 2.59E-06 | 2 | 9 | 0.0154 | 0.00E+00 | ||
8 | 20 | 0.0611 | 5.54E-06 | 39 | 226 | 0.4130 | 3.08E-06 | 2 | 11 | 0.0190 | 0.00E+00 | ||
8 | 19 | 0.0831 | 1.95E-06 | 22 | 99 | 0.1434 | 5.73E-06 | 4 | 15 | 0.0251 | 0.00E+00 | ||
8 | 20 | 0.0651 | 5.54E-06 | 24 | 126 | 0.1656 | 2.59E-06 | 2 | 11 | 0.0175 | 0.00E+00 | ||
8 | 20 | 0.0476 | 5.55E-06 | 35 | 216 | 0.3063 | 8.62E-06 | 2 | 11 | 0.0242 | 0.00E+00 | ||
5 | 14 | 0.0956 | 2.37E-07 | 15 | 60 | 0.1038 | 4.70E-06 | 2 | 9 | 0.0256 | 0.00E+00 | ||
4 | 11 | 0.0494 | 3.25E-08 | 9 | 34 | 0.0697 | 5.29E-06 | 4 | 15 | 0.0457 | 0.00E+00 | ||
15 | 35 | 0.2145 | 6.05E-06 | 13 | 54 | 3.1315 | 7.55E-06 | 5 | 20 | 0.0614 | 0.00E+00 | ||
6 | 16 | 0.0723 | 5.75E-06 | 52 | 336 | 0.7500 | 6.45E-06 | 2 | 9 | 0.0262 | 0.00E+00 | ||
8 | 20 | 0.1135 | 7.84E-06 | 39 | 257 | 0.8268 | 7.40E-06 | 2 | 11 | 0.0234 | 0.00E+00 | ||
8 | 19 | 0.1167 | 1.95E-06 | 21 | 97 | 0.1880 | 7.11E-06 | 4 | 15 | 0.0360 | 0.00E+00 | ||
8 | 20 | 0.1115 | 7.84E-06 | 58 | 456 | 0.8633 | 8.74E-06 | 2 | 11 | 0.0253 | 0.00E+00 | ||
8 | 20 | 0.1302 | 7.84E-06 | 40 | 250 | 0.3797 | 4.87E-06 | 2 | 11 | 0.0324 | 0.00E+00 | ||
7 | 23 | 0.3971 | 9.16E-11 | 14 | 56 | 0.2812 | 4.32E-06 | 3 | 16 | 0.1857 | 0.00E+00 | ||
4 | 11 | 0.1609 | 7.25E-08 | 10 | 38 | 0.3246 | 3.24E-06 | 4 | 15 | 0.1384 | 0.00E+00 | ||
15 | 35 | 0.6173 | 6.05E-06 | 13 | 54 | 25.8148 | 7.55E-06 | 5 | 20 | 0.1416 | 0.00E+00 | ||
7 | 23 | 0.4199 | 7.98E-10 | 41 | 287 | 2.6315 | 4.61E-06 | 2 | 13 | 0.1230 | 0.00E+00 | ||
9 | 23 | 0.3295 | 2.21E-06 | 43 | 261 | 7.0197 | 8.15E-06 | 2 | 10 | 0.0809 | 0.00E+00 | ||
8 | 19 | 0.4273 | 1.95E-06 | 23 | 121 | 0.3488 | 2.56E-06 | 4 | 15 | 0.1403 | 0.00E+00 | ||
9 | 23 | 0.4588 | 2.21E-06 | 42 | 295 | 2.2382 | 7.02E-06 | 3 | 13 | 0.1398 | 0.00E+00 | ||
9 | 23 | 0.3960 | 2.21E-06 | 41 | 252 | 2.0126 | 5.39E-07 | 3 | 13 | 0.1062 | 0.00E+00 | ||
7 | 27 | 0.9775 | 3.55E-07 | 14 | 56 | 0.5772 | 4.93E-06 | 3 | 18 | 0.5132 | 0.00E+00 | ||
4 | 11 | 0.4880 | 1.03E-07 | 10 | 38 | 0.5872 | 4.73E-06 | 4 | 15 | 0.2445 | 0.00E+00 | ||
15 | 35 | 1.0573 | 6.05E-06 | 13 | 54 | 87.3280 | 7.55E-06 | 5 | 20 | 0.3240 | 0.00E+00 | ||
7 | 27 | 0.5609 | 3.63E-06 | 41 | 265 | 3.9792 | 2.29E-06 | 3 | 18 | 0.4003 | 0.00E+00 | ||
9 | 24 | 1.1510 | 4.99E-06 | 52 | 420 | 13.2180 | 1.53E-06 | 2 | 10 | 0.2150 | 0.00E+00 | ||
11 | 25 | 0.7559 | 9.20E-08 | 21 | 99 | 1.2739 | 4.64E-06 | 4 | 15 | 0.2824 | 0.00E+00 | ||
9 | 24 | 1.0529 | 4.99E-06 | 41 | 266 | 3.6878 | 6.90E-06 | 3 | 13 | 0.1655 | 0.00E+00 | ||
9 | 24 | 0.8091 | 4.99E-06 | 42 | 316 | 15.6351 | 3.58E-06 | 3 | 13 | 0.2459 | 0.00E+00 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 5 | 14 | 0.2355 | 8.79E-08 | 16 | 69 | 0.0200 | 4.84E-06 | 2 | 9 | 0.0085 | 0.00E+00 | |
4 | 11 | 0.0156 | 1.06E-08 | 10 | 40 | 0.0126 | 5.44E-06 | 4 | 15 | 0.0079 | 0.00E+00 | ||
15 | 35 | 0.0887 | 6.01E-06 | 13 | 54 | 0.1723 | 7.55E-06 | 5 | 20 | 0.0119 | 0.00E+00 | ||
6 | 16 | 0.0204 | 5.47E-06 | 25 | 133 | 0.1284 | 3.35E-06 | 2 | 9 | 0.0079 | 0.00E+00 | ||
8 | 20 | 0.0294 | 2.47E-06 | 27 | 138 | 0.0757 | 6.03E-06 | 2 | 11 | 0.0076 | 0.00E+00 | ||
8 | 19 | 0.0362 | 1.95E-06 | 26 | 134 | 0.0350 | 4.52E-06 | 4 | 15 | 0.0102 | 0.00E+00 | ||
8 | 20 | 0.0292 | 2.48E-06 | 25 | 133 | 0.1248 | 3.35E-06 | 2 | 11 | 0.0071 | 0.00E+00 | ||
8 | 20 | 0.0299 | 2.49E-06 | 22 | 112 | 0.0317 | 4.53E-06 | 2 | 11 | 0.0080 | 0.00E+00 | ||
5 | 14 | 0.0720 | 1.71E-07 | 17 | 73 | 0.0820 | 2.67E-06 | 2 | 9 | 0.0143 | 0.00E+00 | ||
4 | 11 | 0.0457 | 2.31E-08 | 8 | 31 | 0.0563 | 8.85E-06 | 4 | 15 | 0.0182 | 0.00E+00 | ||
15 | 35 | 0.0707 | 6.05E-06 | 13 | 54 | 1.5146 | 7.55E-06 | 5 | 20 | 0.0308 | 0.00E+00 | ||
6 | 16 | 0.0492 | 5.61E-06 | 24 | 126 | 0.1178 | 2.59E-06 | 2 | 9 | 0.0154 | 0.00E+00 | ||
8 | 20 | 0.0611 | 5.54E-06 | 39 | 226 | 0.4130 | 3.08E-06 | 2 | 11 | 0.0190 | 0.00E+00 | ||
8 | 19 | 0.0831 | 1.95E-06 | 22 | 99 | 0.1434 | 5.73E-06 | 4 | 15 | 0.0251 | 0.00E+00 | ||
8 | 20 | 0.0651 | 5.54E-06 | 24 | 126 | 0.1656 | 2.59E-06 | 2 | 11 | 0.0175 | 0.00E+00 | ||
8 | 20 | 0.0476 | 5.55E-06 | 35 | 216 | 0.3063 | 8.62E-06 | 2 | 11 | 0.0242 | 0.00E+00 | ||
5 | 14 | 0.0956 | 2.37E-07 | 15 | 60 | 0.1038 | 4.70E-06 | 2 | 9 | 0.0256 | 0.00E+00 | ||
4 | 11 | 0.0494 | 3.25E-08 | 9 | 34 | 0.0697 | 5.29E-06 | 4 | 15 | 0.0457 | 0.00E+00 | ||
15 | 35 | 0.2145 | 6.05E-06 | 13 | 54 | 3.1315 | 7.55E-06 | 5 | 20 | 0.0614 | 0.00E+00 | ||
6 | 16 | 0.0723 | 5.75E-06 | 52 | 336 | 0.7500 | 6.45E-06 | 2 | 9 | 0.0262 | 0.00E+00 | ||
8 | 20 | 0.1135 | 7.84E-06 | 39 | 257 | 0.8268 | 7.40E-06 | 2 | 11 | 0.0234 | 0.00E+00 | ||
8 | 19 | 0.1167 | 1.95E-06 | 21 | 97 | 0.1880 | 7.11E-06 | 4 | 15 | 0.0360 | 0.00E+00 | ||
8 | 20 | 0.1115 | 7.84E-06 | 58 | 456 | 0.8633 | 8.74E-06 | 2 | 11 | 0.0253 | 0.00E+00 | ||
8 | 20 | 0.1302 | 7.84E-06 | 40 | 250 | 0.3797 | 4.87E-06 | 2 | 11 | 0.0324 | 0.00E+00 | ||
7 | 23 | 0.3971 | 9.16E-11 | 14 | 56 | 0.2812 | 4.32E-06 | 3 | 16 | 0.1857 | 0.00E+00 | ||
4 | 11 | 0.1609 | 7.25E-08 | 10 | 38 | 0.3246 | 3.24E-06 | 4 | 15 | 0.1384 | 0.00E+00 | ||
15 | 35 | 0.6173 | 6.05E-06 | 13 | 54 | 25.8148 | 7.55E-06 | 5 | 20 | 0.1416 | 0.00E+00 | ||
7 | 23 | 0.4199 | 7.98E-10 | 41 | 287 | 2.6315 | 4.61E-06 | 2 | 13 | 0.1230 | 0.00E+00 | ||
9 | 23 | 0.3295 | 2.21E-06 | 43 | 261 | 7.0197 | 8.15E-06 | 2 | 10 | 0.0809 | 0.00E+00 | ||
8 | 19 | 0.4273 | 1.95E-06 | 23 | 121 | 0.3488 | 2.56E-06 | 4 | 15 | 0.1403 | 0.00E+00 | ||
9 | 23 | 0.4588 | 2.21E-06 | 42 | 295 | 2.2382 | 7.02E-06 | 3 | 13 | 0.1398 | 0.00E+00 | ||
9 | 23 | 0.3960 | 2.21E-06 | 41 | 252 | 2.0126 | 5.39E-07 | 3 | 13 | 0.1062 | 0.00E+00 | ||
7 | 27 | 0.9775 | 3.55E-07 | 14 | 56 | 0.5772 | 4.93E-06 | 3 | 18 | 0.5132 | 0.00E+00 | ||
4 | 11 | 0.4880 | 1.03E-07 | 10 | 38 | 0.5872 | 4.73E-06 | 4 | 15 | 0.2445 | 0.00E+00 | ||
15 | 35 | 1.0573 | 6.05E-06 | 13 | 54 | 87.3280 | 7.55E-06 | 5 | 20 | 0.3240 | 0.00E+00 | ||
7 | 27 | 0.5609 | 3.63E-06 | 41 | 265 | 3.9792 | 2.29E-06 | 3 | 18 | 0.4003 | 0.00E+00 | ||
9 | 24 | 1.1510 | 4.99E-06 | 52 | 420 | 13.2180 | 1.53E-06 | 2 | 10 | 0.2150 | 0.00E+00 | ||
11 | 25 | 0.7559 | 9.20E-08 | 21 | 99 | 1.2739 | 4.64E-06 | 4 | 15 | 0.2824 | 0.00E+00 | ||
9 | 24 | 1.0529 | 4.99E-06 | 41 | 266 | 3.6878 | 6.90E-06 | 3 | 13 | 0.1655 | 0.00E+00 | ||
9 | 24 | 0.8091 | 4.99E-06 | 42 | 316 | 15.6351 | 3.58E-06 | 3 | 13 | 0.2459 | 0.00E+00 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 9 | 26 | 0.0452 | 4.37E-06 | 13 | 40 | 0.0794 | 3.39E-06 | 19 | 93 | 0.3206 | 9.75E-07 | |
7 | 19 | 0.0244 | 7.69E-06 | 7 | 22 | 0.0300 | 5.13E-06 | 15 | 73 | 0.0934 | 4.17E-07 | ||
8 | 22 | 0.0703 | 3.51E-06 | 11 | 36 | 0.1053 | 3.48E-06 | 15 | 73 | 0.1950 | 4.96E-07 | ||
9 | 26 | 0.0401 | 6.71E-06 | 14 | 46 | 0.0217 | 7.56E-06 | 19 | 93 | 0.0969 | 9.62E-07 | ||
10 | 29 | 0.0461 | 3.13E-06 | 14 | 46 | 0.0238 | 7.56E-06 | 19 | 93 | 0.1020 | 4.80E-07 | ||
9 | 25 | 0.0377 | 6.09E-06 | 10 | 32 | 0.0135 | 8.15E-06 | 16 | 78 | 0.0441 | 6.75E-07 | ||
10 | 29 | 0.0764 | 3.13E-06 | 14 | 46 | 0.0165 | 7.56E-06 | 19 | 93 | 0.0604 | 4.80E-07 | ||
10 | 29 | 0.0419 | 3.13E-06 | 14 | 46 | 0.0264 | 7.53E-06 | 19 | 93 | 0.0568 | 4.81E-07 | ||
9 | 26 | 0.1909 | 9.84E-06 | 13 | 40 | 0.0641 | 7.50E-06 | 20 | 98 | 0.4133 | 8.51E-07 | ||
8 | 22 | 0.0677 | 3.39E-06 | 8 | 25 | 0.0360 | 4.94E-06 | 15 | 73 | 0.1504 | 9.03E-07 | ||
8 | 22 | 0.1055 | 3.51E-06 | 11 | 36 | 1.2062 | 8.57E-06 | 15 | 73 | 0.1302 | 4.89E-07 | ||
10 | 29 | 0.1083 | 2.25E-06 | 35 | 157 | 0.1346 | 7.40E-06 | 20 | 98 | 0.1267 | 8.49E-07 | ||
10 | 29 | 0.1217 | 7.01E-06 | 31 | 138 | 0.4007 | 4.24E-06 | 20 | 98 | 0.1494 | 4.20E-07 | ||
9 | 25 | 0.0721 | 6.02E-06 | 10 | 32 | 0.0487 | 8.13E-06 | 16 | 78 | 0.1823 | 6.64E-07 | ||
10 | 29 | 0.1134 | 7.01E-06 | 31 | 138 | 0.2469 | 4.24E-06 | 20 | 98 | 0.1852 | 4.20E-07 | ||
10 | 29 | 0.0780 | 7.01E-06 | 22 | 88 | 0.3009 | 7.25E-06 | 20 | 98 | 0.1700 | 4.21E-07 | ||
10 | 29 | 0.1738 | 2.79E-06 | 14 | 43 | 0.1073 | 2.89E-06 | 21 | 103 | 0.5148 | 4.80E-07 | ||
8 | 22 | 0.0853 | 4.78E-06 | 8 | 25 | 0.0799 | 6.92E-06 | 16 | 78 | 0.2554 | 5.09E-07 | ||
8 | 22 | 0.0803 | 3.51E-06 | 11 | 36 | 3.0274 | 9.89E-06 | 15 | 73 | 0.1792 | 4.88E-07 | ||
10 | 29 | 0.1861 | 2.99E-06 | 16 | 54 | 0.4752 | 4.83E-06 | 21 | 103 | 0.3229 | 4.79E-07 | ||
10 | 29 | 0.2444 | 9.91E-06 | 16 | 54 | 0.1676 | 4.83E-06 | 20 | 98 | 0.3376 | 5.93E-07 | ||
9 | 25 | 0.2425 | 6.02E-06 | 10 | 32 | 0.0720 | 8.13E-06 | 16 | 78 | 0.2158 | 6.63E-07 | ||
10 | 29 | 0.2000 | 9.91E-06 | 16 | 54 | 0.1314 | 4.83E-06 | 20 | 98 | 0.2923 | 5.93E-07 | ||
10 | 29 | 0.2440 | 9.92E-06 | 16 | 54 | 0.0871 | 4.69E-06 | 20 | 98 | 0.3689 | 5.93E-07 | ||
12 | 39 | 1.0114 | 2.30E-06 | 14 | 43 | 0.4292 | 6.46E-06 | 23 | 116 | 2.6259 | 6.55E-07 | ||
9 | 25 | 0.6191 | 2.13E-06 | 9 | 28 | 0.3785 | 1.05E-06 | 17 | 83 | 0.9079 | 4.53E-07 | ||
8 | 22 | 0.3316 | 3.51E-06 | 12 | 39 | 24.3728 | 3.64E-06 | 15 | 73 | 0.4278 | 4.88E-07 | ||
12 | 39 | 0.6189 | 2.30E-06 | f | f | f | f | 23 | 116 | 1.4482 | 6.55E-07 | ||
11 | 32 | 0.8394 | 4.43E-06 | f | f | f | f | 21 | 103 | 1.7160 | 5.29E-07 | ||
9 | 25 | 0.5946 | 6.01E-06 | 10 | 32 | 1.1865 | 8.12E-06 | 16 | 78 | 0.7065 | 6.62E-07 | ||
11 | 32 | 0.7496 | 4.43E-06 | f | f | f | f | 21 | 103 | 1.1586 | 5.29E-07 | ||
11 | 32 | 0.8790 | 4.44E-06 | f | f | f | f | 21 | 103 | 0.8051 | 5.29E-07 | ||
12 | 45 | 2.1717 | 2.90E-06 | 14 | 43 | 1.1046 | 9.13E-06 | 25 | 130 | 3.6530 | 6.38E-07 | ||
9 | 25 | 1.3327 | 3.02E-06 | 9 | 28 | 0.7541 | 1.49E-06 | 17 | 81 | 1.5444 | 1.60E-11 | ||
8 | 22 | 0.9087 | 3.51E-06 | 12 | 41 | 94.8845 | 3.66E-06 | 15 | 73 | 1.2575 | 4.88E-07 | ||
12 | 45 | 1.7092 | 3.05E-06 | f | f | f | f | 25 | 130 | 1.9217 | 6.38E-07 | ||
13 | 40 | 1.2000 | 2.81E-06 | f | f | f | f | 22 | 110 | 2.0242 | 6.94E-07 | ||
9 | 25 | 1.2705 | 6.01E-06 | 10 | 32 | 0.8082 | 8.12E-06 | 16 | 78 | 1.4797 | 6.62E-07 | ||
13 | 40 | 1.9988 | 2.81E-06 | f | f | f | f | 22 | 110 | 1.7161 | 6.94E-07 | ||
13 | 40 | 1.7253 | 2.81E-06 | f | f | f | f | 22 | 110 | 2.3099 | 6.94E-07 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 9 | 26 | 0.0452 | 4.37E-06 | 13 | 40 | 0.0794 | 3.39E-06 | 19 | 93 | 0.3206 | 9.75E-07 | |
7 | 19 | 0.0244 | 7.69E-06 | 7 | 22 | 0.0300 | 5.13E-06 | 15 | 73 | 0.0934 | 4.17E-07 | ||
8 | 22 | 0.0703 | 3.51E-06 | 11 | 36 | 0.1053 | 3.48E-06 | 15 | 73 | 0.1950 | 4.96E-07 | ||
9 | 26 | 0.0401 | 6.71E-06 | 14 | 46 | 0.0217 | 7.56E-06 | 19 | 93 | 0.0969 | 9.62E-07 | ||
10 | 29 | 0.0461 | 3.13E-06 | 14 | 46 | 0.0238 | 7.56E-06 | 19 | 93 | 0.1020 | 4.80E-07 | ||
9 | 25 | 0.0377 | 6.09E-06 | 10 | 32 | 0.0135 | 8.15E-06 | 16 | 78 | 0.0441 | 6.75E-07 | ||
10 | 29 | 0.0764 | 3.13E-06 | 14 | 46 | 0.0165 | 7.56E-06 | 19 | 93 | 0.0604 | 4.80E-07 | ||
10 | 29 | 0.0419 | 3.13E-06 | 14 | 46 | 0.0264 | 7.53E-06 | 19 | 93 | 0.0568 | 4.81E-07 | ||
9 | 26 | 0.1909 | 9.84E-06 | 13 | 40 | 0.0641 | 7.50E-06 | 20 | 98 | 0.4133 | 8.51E-07 | ||
8 | 22 | 0.0677 | 3.39E-06 | 8 | 25 | 0.0360 | 4.94E-06 | 15 | 73 | 0.1504 | 9.03E-07 | ||
8 | 22 | 0.1055 | 3.51E-06 | 11 | 36 | 1.2062 | 8.57E-06 | 15 | 73 | 0.1302 | 4.89E-07 | ||
10 | 29 | 0.1083 | 2.25E-06 | 35 | 157 | 0.1346 | 7.40E-06 | 20 | 98 | 0.1267 | 8.49E-07 | ||
10 | 29 | 0.1217 | 7.01E-06 | 31 | 138 | 0.4007 | 4.24E-06 | 20 | 98 | 0.1494 | 4.20E-07 | ||
9 | 25 | 0.0721 | 6.02E-06 | 10 | 32 | 0.0487 | 8.13E-06 | 16 | 78 | 0.1823 | 6.64E-07 | ||
10 | 29 | 0.1134 | 7.01E-06 | 31 | 138 | 0.2469 | 4.24E-06 | 20 | 98 | 0.1852 | 4.20E-07 | ||
10 | 29 | 0.0780 | 7.01E-06 | 22 | 88 | 0.3009 | 7.25E-06 | 20 | 98 | 0.1700 | 4.21E-07 | ||
10 | 29 | 0.1738 | 2.79E-06 | 14 | 43 | 0.1073 | 2.89E-06 | 21 | 103 | 0.5148 | 4.80E-07 | ||
8 | 22 | 0.0853 | 4.78E-06 | 8 | 25 | 0.0799 | 6.92E-06 | 16 | 78 | 0.2554 | 5.09E-07 | ||
8 | 22 | 0.0803 | 3.51E-06 | 11 | 36 | 3.0274 | 9.89E-06 | 15 | 73 | 0.1792 | 4.88E-07 | ||
10 | 29 | 0.1861 | 2.99E-06 | 16 | 54 | 0.4752 | 4.83E-06 | 21 | 103 | 0.3229 | 4.79E-07 | ||
10 | 29 | 0.2444 | 9.91E-06 | 16 | 54 | 0.1676 | 4.83E-06 | 20 | 98 | 0.3376 | 5.93E-07 | ||
9 | 25 | 0.2425 | 6.02E-06 | 10 | 32 | 0.0720 | 8.13E-06 | 16 | 78 | 0.2158 | 6.63E-07 | ||
10 | 29 | 0.2000 | 9.91E-06 | 16 | 54 | 0.1314 | 4.83E-06 | 20 | 98 | 0.2923 | 5.93E-07 | ||
10 | 29 | 0.2440 | 9.92E-06 | 16 | 54 | 0.0871 | 4.69E-06 | 20 | 98 | 0.3689 | 5.93E-07 | ||
12 | 39 | 1.0114 | 2.30E-06 | 14 | 43 | 0.4292 | 6.46E-06 | 23 | 116 | 2.6259 | 6.55E-07 | ||
9 | 25 | 0.6191 | 2.13E-06 | 9 | 28 | 0.3785 | 1.05E-06 | 17 | 83 | 0.9079 | 4.53E-07 | ||
8 | 22 | 0.3316 | 3.51E-06 | 12 | 39 | 24.3728 | 3.64E-06 | 15 | 73 | 0.4278 | 4.88E-07 | ||
12 | 39 | 0.6189 | 2.30E-06 | f | f | f | f | 23 | 116 | 1.4482 | 6.55E-07 | ||
11 | 32 | 0.8394 | 4.43E-06 | f | f | f | f | 21 | 103 | 1.7160 | 5.29E-07 | ||
9 | 25 | 0.5946 | 6.01E-06 | 10 | 32 | 1.1865 | 8.12E-06 | 16 | 78 | 0.7065 | 6.62E-07 | ||
11 | 32 | 0.7496 | 4.43E-06 | f | f | f | f | 21 | 103 | 1.1586 | 5.29E-07 | ||
11 | 32 | 0.8790 | 4.44E-06 | f | f | f | f | 21 | 103 | 0.8051 | 5.29E-07 | ||
12 | 45 | 2.1717 | 2.90E-06 | 14 | 43 | 1.1046 | 9.13E-06 | 25 | 130 | 3.6530 | 6.38E-07 | ||
9 | 25 | 1.3327 | 3.02E-06 | 9 | 28 | 0.7541 | 1.49E-06 | 17 | 81 | 1.5444 | 1.60E-11 | ||
8 | 22 | 0.9087 | 3.51E-06 | 12 | 41 | 94.8845 | 3.66E-06 | 15 | 73 | 1.2575 | 4.88E-07 | ||
12 | 45 | 1.7092 | 3.05E-06 | f | f | f | f | 25 | 130 | 1.9217 | 6.38E-07 | ||
13 | 40 | 1.2000 | 2.81E-06 | f | f | f | f | 22 | 110 | 2.0242 | 6.94E-07 | ||
9 | 25 | 1.2705 | 6.01E-06 | 10 | 32 | 0.8082 | 8.12E-06 | 16 | 78 | 1.4797 | 6.62E-07 | ||
13 | 40 | 1.9988 | 2.81E-06 | f | f | f | f | 22 | 110 | 1.7161 | 6.94E-07 | ||
13 | 40 | 1.7253 | 2.81E-06 | f | f | f | f | 22 | 110 | 2.3099 | 6.94E-07 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 4 | 8 | 0.8195 | 6.47E-09 | 12 | 39 | 0.0871 | 9.82E-06 | 2 | 8 | 0.0309 | 0.00E+00 | |
3 | 6 | 0.0912 | 8.25E-08 | 10 | 32 | 0.0564 | 9.57E-06 | 2 | 8 | 0.0068 | 0.00E+00 | ||
13 | 27 | 0.0953 | 8.81E-06 | 9 | 29 | 0.2011 | 2.35E-06 | 13 | 51 | 0.0271 | 3.85E-07 | ||
4 | 8 | 0.0192 | 1.42E-06 | 37 | 210 | 0.1077 | 2.98E-06 | 17 | 69 | 0.0250 | 7.21E-07 | ||
6 | 12 | 0.0705 | 5.56E-06 | 37 | 210 | 0.0689 | 2.98E-06 | 17 | 73 | 0.0373 | 8.83E-07 | ||
5 | 10 | 0.0919 | 6.68E-11 | 16 | 56 | 0.0211 | 7.32E-06 | 15 | 59 | 0.0292 | 8.78E-07 | ||
6 | 12 | 0.0203 | 5.56E-06 | 37 | 210 | 0.0639 | 2.98E-06 | 17 | 73 | 0.0332 | 8.83E-07 | ||
8 | 16 | 0.1217 | 4.35E-08 | 19 | 85 | 0.0470 | 6.92E-06 | 17 | 73 | 0.0263 | 8.83E-07 | ||
4 | 8 | 0.0746 | 1.45E-08 | 13 | 42 | 0.0529 | 3.54E-06 | 2 | 8 | 0.0133 | 0.00E+00 | ||
3 | 6 | 0.0249 | 1.84E-07 | 11 | 35 | 0.0574 | 3.71E-06 | 2 | 8 | 0.0097 | 0.00E+00 | ||
13 | 27 | 0.1299 | 8.81E-06 | 9 | 29 | 1.1781 | 2.35E-06 | 13 | 51 | 0.0781 | 3.85E-07 | ||
4 | 8 | 0.0397 | 1.28E-06 | 36 | 209 | 0.4912 | 3.49E-06 | 18 | 72 | 0.0891 | 3.15E-07 | ||
13 | 26 | 0.0749 | 7.27E-13 | 36 | 209 | 0.3499 | 3.49E-06 | 18 | 76 | 0.1789 | 6.06E-07 | ||
5 | 10 | 0.0320 | 6.70E-11 | 21 | 81 | 0.1014 | 7.63E-06 | 16 | 62 | 0.0643 | 9.17E-07 | ||
13 | 26 | 0.0643 | 7.27E-13 | 36 | 209 | 0.3509 | 3.49E-06 | 18 | 76 | 0.1192 | 6.08E-07 | ||
9 | 18 | 0.0524 | 8.51E-09 | 20 | 84 | 0.1209 | 8.44E-06 | 18 | 76 | 0.0923 | 6.07E-07 | ||
4 | 8 | 0.3372 | 2.04E-08 | 13 | 42 | 0.0841 | 5.00E-06 | 2 | 8 | 0.0186 | 0.00E+00 | ||
3 | 6 | 0.0404 | 2.61E-07 | 11 | 35 | 0.0801 | 5.24E-06 | 2 | 8 | 0.0165 | 0.00E+00 | ||
13 | 27 | 0.1017 | 8.81E-06 | 9 | 29 | 3.2921 | 2.35E-06 | 13 | 51 | 0.0892 | 3.85E-07 | ||
4 | 8 | 0.0452 | 1.30E-06 | 31 | 177 | 0.4489 | 1.82E-06 | 15 | 59 | 0.0737 | 8.90E-07 | ||
11 | 22 | 0.1231 | 1.43E-10 | 31 | 177 | 0.3576 | 1.82E-06 | 18 | 76 | 0.0882 | 8.57E-07 | ||
5 | 10 | 0.0408 | 6.70E-11 | 18 | 72 | 0.1468 | 8.19E-06 | f | f | f | f | ||
11 | 22 | 0.0840 | 1.43E-10 | 31 | 177 | 0.3460 | 1.82E-06 | 18 | 76 | 0.1498 | 8.57E-07 | ||
12 | 24 | 0.0726 | 1.21E-11 | 29 | 153 | 0.3801 | 6.17E-06 | 18 | 76 | 0.1678 | 8.55E-07 | ||
5 | 15 | 0.1876 | 1.58E-06 | 14 | 45 | 0.3743 | 4.52E-06 | 3 | 14 | 0.2255 | 0.00E+00 | ||
3 | 6 | 0.1362 | 5.83E-07 | 12 | 38 | 0.3290 | 4.63E-06 | 2 | 8 | 0.1014 | 0.00E+00 | ||
13 | 27 | 0.4447 | 8.81E-06 | 9 | 29 | 22.4652 | 2.35E-06 | 13 | 51 | 0.3770 | 3.85E-07 | ||
6 | 17 | 0.3568 | 2.93E-10 | 40 | 278 | 8.4671 | 7.10E-06 | 18 | 73 | 0.6564 | 6.79E-07 | ||
17 | 36 | 0.6444 | 7.27E-06 | 40 | 278 | 9.2475 | 7.10E-06 | f | f | f | f | ||
5 | 10 | 0.1576 | 6.71E-11 | 21 | 80 | 4.8421 | 9.53E-06 | f | f | f | f | ||
17 | 36 | 0.4210 | 7.27E-06 | 40 | 278 | 8.9672 | 7.10E-06 | f | f | f | f | ||
17 | 36 | 0.4061 | 7.27E-06 | 36 | 222 | 0.7206 | 4.06E-06 | f | f | f | f | ||
6 | 21 | 0.9043 | 8.13E-09 | 14 | 45 | 0.3008 | 6.39E-06 | 4 | 21 | 0.2761 | 0.00E+00 | ||
3 | 6 | 0.2392 | 8.25E-07 | 12 | 38 | 0.6761 | 6.55E-06 | 2 | 8 | 0.1008 | 0.00E+00 | ||
13 | 27 | 0.5491 | 8.81E-06 | 9 | 29 | 72.1280 | 2.35E-06 | 13 | 51 | 0.5589 | 3.85E-07 | ||
6 | 21 | 0.4396 | 1.81E-08 | 34 | 224 | 3.5081 | 4.61E-06 | 19 | 80 | 1.1189 | 6.33E-07 | ||
18 | 40 | 1.4053 | 7.38E-06 | 34 | 224 | 2.4146 | 4.61E-06 | f | f | f | f | ||
5 | 10 | 0.3521 | 6.71E-11 | 19 | 71 | 7.7563 | 4.00E-06 | f | f | f | f | ||
18 | 40 | 1.0043 | 7.38E-06 | 34 | 224 | 3.4369 | 4.61E-06 | f | f | f | f | ||
18 | 40 | 1.2596 | 7.38E-06 | 37 | 225 | 3.3577 | 4.58E-06 | f | f | f | f |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 4 | 8 | 0.8195 | 6.47E-09 | 12 | 39 | 0.0871 | 9.82E-06 | 2 | 8 | 0.0309 | 0.00E+00 | |
3 | 6 | 0.0912 | 8.25E-08 | 10 | 32 | 0.0564 | 9.57E-06 | 2 | 8 | 0.0068 | 0.00E+00 | ||
13 | 27 | 0.0953 | 8.81E-06 | 9 | 29 | 0.2011 | 2.35E-06 | 13 | 51 | 0.0271 | 3.85E-07 | ||
4 | 8 | 0.0192 | 1.42E-06 | 37 | 210 | 0.1077 | 2.98E-06 | 17 | 69 | 0.0250 | 7.21E-07 | ||
6 | 12 | 0.0705 | 5.56E-06 | 37 | 210 | 0.0689 | 2.98E-06 | 17 | 73 | 0.0373 | 8.83E-07 | ||
5 | 10 | 0.0919 | 6.68E-11 | 16 | 56 | 0.0211 | 7.32E-06 | 15 | 59 | 0.0292 | 8.78E-07 | ||
6 | 12 | 0.0203 | 5.56E-06 | 37 | 210 | 0.0639 | 2.98E-06 | 17 | 73 | 0.0332 | 8.83E-07 | ||
8 | 16 | 0.1217 | 4.35E-08 | 19 | 85 | 0.0470 | 6.92E-06 | 17 | 73 | 0.0263 | 8.83E-07 | ||
4 | 8 | 0.0746 | 1.45E-08 | 13 | 42 | 0.0529 | 3.54E-06 | 2 | 8 | 0.0133 | 0.00E+00 | ||
3 | 6 | 0.0249 | 1.84E-07 | 11 | 35 | 0.0574 | 3.71E-06 | 2 | 8 | 0.0097 | 0.00E+00 | ||
13 | 27 | 0.1299 | 8.81E-06 | 9 | 29 | 1.1781 | 2.35E-06 | 13 | 51 | 0.0781 | 3.85E-07 | ||
4 | 8 | 0.0397 | 1.28E-06 | 36 | 209 | 0.4912 | 3.49E-06 | 18 | 72 | 0.0891 | 3.15E-07 | ||
13 | 26 | 0.0749 | 7.27E-13 | 36 | 209 | 0.3499 | 3.49E-06 | 18 | 76 | 0.1789 | 6.06E-07 | ||
5 | 10 | 0.0320 | 6.70E-11 | 21 | 81 | 0.1014 | 7.63E-06 | 16 | 62 | 0.0643 | 9.17E-07 | ||
13 | 26 | 0.0643 | 7.27E-13 | 36 | 209 | 0.3509 | 3.49E-06 | 18 | 76 | 0.1192 | 6.08E-07 | ||
9 | 18 | 0.0524 | 8.51E-09 | 20 | 84 | 0.1209 | 8.44E-06 | 18 | 76 | 0.0923 | 6.07E-07 | ||
4 | 8 | 0.3372 | 2.04E-08 | 13 | 42 | 0.0841 | 5.00E-06 | 2 | 8 | 0.0186 | 0.00E+00 | ||
3 | 6 | 0.0404 | 2.61E-07 | 11 | 35 | 0.0801 | 5.24E-06 | 2 | 8 | 0.0165 | 0.00E+00 | ||
13 | 27 | 0.1017 | 8.81E-06 | 9 | 29 | 3.2921 | 2.35E-06 | 13 | 51 | 0.0892 | 3.85E-07 | ||
4 | 8 | 0.0452 | 1.30E-06 | 31 | 177 | 0.4489 | 1.82E-06 | 15 | 59 | 0.0737 | 8.90E-07 | ||
11 | 22 | 0.1231 | 1.43E-10 | 31 | 177 | 0.3576 | 1.82E-06 | 18 | 76 | 0.0882 | 8.57E-07 | ||
5 | 10 | 0.0408 | 6.70E-11 | 18 | 72 | 0.1468 | 8.19E-06 | f | f | f | f | ||
11 | 22 | 0.0840 | 1.43E-10 | 31 | 177 | 0.3460 | 1.82E-06 | 18 | 76 | 0.1498 | 8.57E-07 | ||
12 | 24 | 0.0726 | 1.21E-11 | 29 | 153 | 0.3801 | 6.17E-06 | 18 | 76 | 0.1678 | 8.55E-07 | ||
5 | 15 | 0.1876 | 1.58E-06 | 14 | 45 | 0.3743 | 4.52E-06 | 3 | 14 | 0.2255 | 0.00E+00 | ||
3 | 6 | 0.1362 | 5.83E-07 | 12 | 38 | 0.3290 | 4.63E-06 | 2 | 8 | 0.1014 | 0.00E+00 | ||
13 | 27 | 0.4447 | 8.81E-06 | 9 | 29 | 22.4652 | 2.35E-06 | 13 | 51 | 0.3770 | 3.85E-07 | ||
6 | 17 | 0.3568 | 2.93E-10 | 40 | 278 | 8.4671 | 7.10E-06 | 18 | 73 | 0.6564 | 6.79E-07 | ||
17 | 36 | 0.6444 | 7.27E-06 | 40 | 278 | 9.2475 | 7.10E-06 | f | f | f | f | ||
5 | 10 | 0.1576 | 6.71E-11 | 21 | 80 | 4.8421 | 9.53E-06 | f | f | f | f | ||
17 | 36 | 0.4210 | 7.27E-06 | 40 | 278 | 8.9672 | 7.10E-06 | f | f | f | f | ||
17 | 36 | 0.4061 | 7.27E-06 | 36 | 222 | 0.7206 | 4.06E-06 | f | f | f | f | ||
6 | 21 | 0.9043 | 8.13E-09 | 14 | 45 | 0.3008 | 6.39E-06 | 4 | 21 | 0.2761 | 0.00E+00 | ||
3 | 6 | 0.2392 | 8.25E-07 | 12 | 38 | 0.6761 | 6.55E-06 | 2 | 8 | 0.1008 | 0.00E+00 | ||
13 | 27 | 0.5491 | 8.81E-06 | 9 | 29 | 72.1280 | 2.35E-06 | 13 | 51 | 0.5589 | 3.85E-07 | ||
6 | 21 | 0.4396 | 1.81E-08 | 34 | 224 | 3.5081 | 4.61E-06 | 19 | 80 | 1.1189 | 6.33E-07 | ||
18 | 40 | 1.4053 | 7.38E-06 | 34 | 224 | 2.4146 | 4.61E-06 | f | f | f | f | ||
5 | 10 | 0.3521 | 6.71E-11 | 19 | 71 | 7.7563 | 4.00E-06 | f | f | f | f | ||
18 | 40 | 1.0043 | 7.38E-06 | 34 | 224 | 3.4369 | 4.61E-06 | f | f | f | f | ||
18 | 40 | 1.2596 | 7.38E-06 | 37 | 225 | 3.3577 | 4.58E-06 | f | f | f | f |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 10 | 29 | 0.1975 | 5.56E-06 | 13 | 41 | 0.0277 | 2.04E-06 | 17 | 83 | 0.0574 | 5.78E-07 | |
10 | 29 | 0.0528 | 8.48E-06 | 13 | 41 | 0.0191 | 3.11E-06 | 19 | 89 | 0.0732 | 7.34E-07 | ||
10 | 28 | 0.0530 | 1.66E-14 | 13 | 41 | 0.0182 | 3.22E-06 | f | f | f | f | ||
10 | 28 | 0.0521 | 1.31E-14 | 13 | 41 | 0.0229 | 2.65E-06 | f | f | f | f | ||
10 | 28 | 0.0362 | 1.23E-14 | 13 | 41 | 0.0206 | 2.65E-06 | 20 | 92 | 0.0418 | 6.37E-07 | ||
10 | 28 | 0.0370 | 1.12E-14 | 13 | 41 | 0.0291 | 3.22E-06 | 17 | 83 | 0.0544 | 7.43E-07 | ||
10 | 28 | 0.0345 | 1.23E-14 | 13 | 41 | 0.0273 | 2.65E-06 | 20 | 92 | 0.0623 | 6.37E-07 | ||
10 | 28 | 0.0388 | 1.16E-14 | 13 | 41 | 0.0181 | 2.65E-06 | 20 | 92 | 0.0504 | 6.37E-07 | ||
11 | 32 | 0.1438 | 2.49E-06 | 13 | 41 | 0.2237 | 4.56E-06 | f | f | f | f | ||
10 | 30 | 0.1277 | 0.00E+00 | 13 | 41 | 0.2464 | 6.96E-06 | 657 | 2006 | 2.2801 | 4.71E-07 | ||
11 | 34 | 0.1592 | 9.60E-06 | 13 | 41 | 0.0676 | 7.22E-06 | 21 | 104 | 0.2050 | 3.40E-08 | ||
11 | 32 | 0.1546 | 2.49E-06 | 13 | 41 | 0.0814 | 5.94E-06 | 17 | 83 | 0.1518 | 8.10E-07 | ||
11 | 34 | 0.0902 | 7.90E-06 | 13 | 41 | 0.1253 | 5.94E-06 | 21 | 105 | 0.1327 | 6.96E-07 | ||
11 | 34 | 0.2370 | 9.60E-06 | 13 | 41 | 0.0804 | 7.22E-06 | 19 | 94 | 0.1391 | 1.91E-07 | ||
11 | 34 | 0.1372 | 7.90E-06 | 13 | 41 | 0.0817 | 5.94E-06 | 21 | 105 | 0.1985 | 6.96E-07 | ||
11 | 34 | 0.1759 | 7.90E-06 | 13 | 41 | 0.0618 | 5.94E-06 | 21 | 105 | 0.1921 | 6.96E-07 | ||
10 | 30 | 0.3047 | 8.88E-16 | 13 | 41 | 0.1117 | 6.46E-06 | 248 | 777 | 2.4396 | 7.71E-07 | ||
12 | 41 | 0.4791 | 8.80E-06 | 13 | 41 | 0.2053 | 9.84E-06 | 321 | 999 | 3.1750 | 7.52E-07 | ||
11 | 37 | 0.2859 | 1.33E-15 | 14 | 44 | 0.2424 | 4.02E-06 | f | f | f | f | ||
11 | 34 | 0.2346 | 8.59E-06 | 13 | 41 | 0.1677 | 8.41E-06 | 27 | 116 | 0.1964 | 4.43E-07 | ||
12 | 39 | 0.3669 | 4.87E-06 | 13 | 41 | 0.1120 | 8.41E-06 | 22 | 111 | 0.4084 | 6.30E-07 | ||
12 | 41 | 0.2340 | 9.13E-06 | 14 | 44 | 0.1076 | 4.02E-06 | 240 | 756 | 2.1246 | 6.20E-07 | ||
12 | 39 | 0.3153 | 4.87E-06 | 13 | 41 | 0.1737 | 8.41E-06 | 22 | 111 | 0.5055 | 6.30E-07 | ||
12 | 39 | 0.3989 | 4.87E-06 | 13 | 41 | 0.1488 | 8.40E-06 | 22 | 111 | 0.3394 | 6.30E-07 | ||
9 | 38 | 0.8360 | 0.00E+00 | 14 | 44 | 0.6011 | 5.69E-06 | 22 | 107 | 1.0331 | 4.71E-07 | ||
13 | 66 | 1.4044 | 9.93E-14 | 14 | 44 | 0.7478 | 8.67E-06 | 23 | 121 | 1.4131 | 8.76E-07 | ||
13 | 69 | 1.1444 | 9.93E-16 | 14 | 44 | 0.7075 | 9.00E-06 | 29 | 140 | 1.7453 | 9.92E-07 | ||
10 | 41 | 1.0490 | 2.03E-14 | 14 | 44 | 0.5255 | 7.40E-06 | f | f | f | f | ||
11 | 53 | 1.4307 | 4.86E-14 | 14 | 44 | 0.6108 | 7.40E-06 | 277 | 878 | 5.8666 | 8.74E-07 | ||
14 | 72 | 1.6761 | 7.15E-15 | 14 | 44 | 0.6519 | 9.00E-06 | f | f | f | f | ||
11 | 53 | 1.0887 | 4.86E-14 | 14 | 44 | 0.5013 | 7.40E-06 | 277 | 878 | 5.8247 | 8.74E-07 | ||
11 | 53 | 0.9404 | 4.86E-14 | 14 | 44 | 0.6483 | 7.40E-06 | 23 | 116 | 1.6068 | 8.75E-07 | ||
13 | 61 | 2.9900 | 1.40E-13 | 14 | 44 | 1.2238 | 8.04E-06 | 21 | 114 | 2.6706 | 4.32E-07 | ||
15 | 92 | 4.1893 | 1.40E-13 | 15 | 47 | 1.0116 | 2.14E-06 | 24 | 140 | 3.1769 | 7.35E-07 | ||
15 | 98 | 3.8911 | 1.40E-13 | 15 | 47 | 1.2457 | 2.23E-06 | 29 | 158 | 2.5033 | 8.14E-07 | ||
11 | 55 | 2.2741 | 1.72E-14 | 15 | 47 | 1.3337 | 1.83E-06 | 21 | 114 | 1.5601 | 6.03E-07 | ||
13 | 77 | 3.0852 | 9.15E-14 | 15 | 47 | 1.4839 | 1.83E-06 | 75 | 284 | 7.6840 | 8.99E-07 | ||
15 | 98 | 3.7006 | 1.33E-13 | 15 | 47 | 1.2636 | 2.23E-06 | 567 | 1772 | 31.9028 | 7.18E-07 | ||
13 | 77 | 3.3259 | 9.15E-14 | 15 | 47 | 1.3969 | 1.83E-06 | 75 | 284 | 5.1793 | 8.99E-07 | ||
13 | 77 | 2.3221 | 9.15E-14 | 15 | 47 | 1.4001 | 1.83E-06 | 75 | 284 | 5.6734 | 8.99E-07 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 10 | 29 | 0.1975 | 5.56E-06 | 13 | 41 | 0.0277 | 2.04E-06 | 17 | 83 | 0.0574 | 5.78E-07 | |
10 | 29 | 0.0528 | 8.48E-06 | 13 | 41 | 0.0191 | 3.11E-06 | 19 | 89 | 0.0732 | 7.34E-07 | ||
10 | 28 | 0.0530 | 1.66E-14 | 13 | 41 | 0.0182 | 3.22E-06 | f | f | f | f | ||
10 | 28 | 0.0521 | 1.31E-14 | 13 | 41 | 0.0229 | 2.65E-06 | f | f | f | f | ||
10 | 28 | 0.0362 | 1.23E-14 | 13 | 41 | 0.0206 | 2.65E-06 | 20 | 92 | 0.0418 | 6.37E-07 | ||
10 | 28 | 0.0370 | 1.12E-14 | 13 | 41 | 0.0291 | 3.22E-06 | 17 | 83 | 0.0544 | 7.43E-07 | ||
10 | 28 | 0.0345 | 1.23E-14 | 13 | 41 | 0.0273 | 2.65E-06 | 20 | 92 | 0.0623 | 6.37E-07 | ||
10 | 28 | 0.0388 | 1.16E-14 | 13 | 41 | 0.0181 | 2.65E-06 | 20 | 92 | 0.0504 | 6.37E-07 | ||
11 | 32 | 0.1438 | 2.49E-06 | 13 | 41 | 0.2237 | 4.56E-06 | f | f | f | f | ||
10 | 30 | 0.1277 | 0.00E+00 | 13 | 41 | 0.2464 | 6.96E-06 | 657 | 2006 | 2.2801 | 4.71E-07 | ||
11 | 34 | 0.1592 | 9.60E-06 | 13 | 41 | 0.0676 | 7.22E-06 | 21 | 104 | 0.2050 | 3.40E-08 | ||
11 | 32 | 0.1546 | 2.49E-06 | 13 | 41 | 0.0814 | 5.94E-06 | 17 | 83 | 0.1518 | 8.10E-07 | ||
11 | 34 | 0.0902 | 7.90E-06 | 13 | 41 | 0.1253 | 5.94E-06 | 21 | 105 | 0.1327 | 6.96E-07 | ||
11 | 34 | 0.2370 | 9.60E-06 | 13 | 41 | 0.0804 | 7.22E-06 | 19 | 94 | 0.1391 | 1.91E-07 | ||
11 | 34 | 0.1372 | 7.90E-06 | 13 | 41 | 0.0817 | 5.94E-06 | 21 | 105 | 0.1985 | 6.96E-07 | ||
11 | 34 | 0.1759 | 7.90E-06 | 13 | 41 | 0.0618 | 5.94E-06 | 21 | 105 | 0.1921 | 6.96E-07 | ||
10 | 30 | 0.3047 | 8.88E-16 | 13 | 41 | 0.1117 | 6.46E-06 | 248 | 777 | 2.4396 | 7.71E-07 | ||
12 | 41 | 0.4791 | 8.80E-06 | 13 | 41 | 0.2053 | 9.84E-06 | 321 | 999 | 3.1750 | 7.52E-07 | ||
11 | 37 | 0.2859 | 1.33E-15 | 14 | 44 | 0.2424 | 4.02E-06 | f | f | f | f | ||
11 | 34 | 0.2346 | 8.59E-06 | 13 | 41 | 0.1677 | 8.41E-06 | 27 | 116 | 0.1964 | 4.43E-07 | ||
12 | 39 | 0.3669 | 4.87E-06 | 13 | 41 | 0.1120 | 8.41E-06 | 22 | 111 | 0.4084 | 6.30E-07 | ||
12 | 41 | 0.2340 | 9.13E-06 | 14 | 44 | 0.1076 | 4.02E-06 | 240 | 756 | 2.1246 | 6.20E-07 | ||
12 | 39 | 0.3153 | 4.87E-06 | 13 | 41 | 0.1737 | 8.41E-06 | 22 | 111 | 0.5055 | 6.30E-07 | ||
12 | 39 | 0.3989 | 4.87E-06 | 13 | 41 | 0.1488 | 8.40E-06 | 22 | 111 | 0.3394 | 6.30E-07 | ||
9 | 38 | 0.8360 | 0.00E+00 | 14 | 44 | 0.6011 | 5.69E-06 | 22 | 107 | 1.0331 | 4.71E-07 | ||
13 | 66 | 1.4044 | 9.93E-14 | 14 | 44 | 0.7478 | 8.67E-06 | 23 | 121 | 1.4131 | 8.76E-07 | ||
13 | 69 | 1.1444 | 9.93E-16 | 14 | 44 | 0.7075 | 9.00E-06 | 29 | 140 | 1.7453 | 9.92E-07 | ||
10 | 41 | 1.0490 | 2.03E-14 | 14 | 44 | 0.5255 | 7.40E-06 | f | f | f | f | ||
11 | 53 | 1.4307 | 4.86E-14 | 14 | 44 | 0.6108 | 7.40E-06 | 277 | 878 | 5.8666 | 8.74E-07 | ||
14 | 72 | 1.6761 | 7.15E-15 | 14 | 44 | 0.6519 | 9.00E-06 | f | f | f | f | ||
11 | 53 | 1.0887 | 4.86E-14 | 14 | 44 | 0.5013 | 7.40E-06 | 277 | 878 | 5.8247 | 8.74E-07 | ||
11 | 53 | 0.9404 | 4.86E-14 | 14 | 44 | 0.6483 | 7.40E-06 | 23 | 116 | 1.6068 | 8.75E-07 | ||
13 | 61 | 2.9900 | 1.40E-13 | 14 | 44 | 1.2238 | 8.04E-06 | 21 | 114 | 2.6706 | 4.32E-07 | ||
15 | 92 | 4.1893 | 1.40E-13 | 15 | 47 | 1.0116 | 2.14E-06 | 24 | 140 | 3.1769 | 7.35E-07 | ||
15 | 98 | 3.8911 | 1.40E-13 | 15 | 47 | 1.2457 | 2.23E-06 | 29 | 158 | 2.5033 | 8.14E-07 | ||
11 | 55 | 2.2741 | 1.72E-14 | 15 | 47 | 1.3337 | 1.83E-06 | 21 | 114 | 1.5601 | 6.03E-07 | ||
13 | 77 | 3.0852 | 9.15E-14 | 15 | 47 | 1.4839 | 1.83E-06 | 75 | 284 | 7.6840 | 8.99E-07 | ||
15 | 98 | 3.7006 | 1.33E-13 | 15 | 47 | 1.2636 | 2.23E-06 | 567 | 1772 | 31.9028 | 7.18E-07 | ||
13 | 77 | 3.3259 | 9.15E-14 | 15 | 47 | 1.3969 | 1.83E-06 | 75 | 284 | 5.1793 | 8.99E-07 | ||
13 | 77 | 2.3221 | 9.15E-14 | 15 | 47 | 1.4001 | 1.83E-06 | 75 | 284 | 5.6734 | 8.99E-07 |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 5 | 12 | 0.2244 | 3.26E-06 | 11 | 38 | 0.2095 | 3.21E-06 | 2 | 9 | 0.0260 | 0.00E+00 | |
4 | 8 | 0.1030 | 7.57E-08 | 9 | 29 | 0.0294 | 8.71E-06 | 2 | 8 | 0.0143 | 0.00E+00 | ||
5 | 11 | 0.0745 | 1.28E-07 | 12 | 38 | 0.1401 | 1.70E-06 | 4 | 14 | 0.0322 | 2.22E-16 | ||
7 | 16 | 0.0238 | 1.92E-06 | 21 | 79 | 0.0319 | 6.66E-06 | 12 | 45 | 0.0305 | 7.78E-08 | ||
9 | 19 | 0.0954 | 6.02E-06 | 21 | 79 | 0.0333 | 6.66E-06 | 14 | 54 | 0.0385 | 3.41E-07 | ||
9 | 19 | 0.0316 | 4.09E-06 | 11 | 36 | 0.0131 | 3.32E-06 | 14 | 54 | 0.0249 | 2.67E-07 | ||
9 | 19 | 0.0215 | 6.02E-06 | 21 | 79 | 0.0265 | 6.66E-06 | 14 | 54 | 0.0204 | 3.42E-07 | ||
9 | 19 | 0.0286 | 5.97E-06 | 17 | 61 | 0.0164 | 6.86E-06 | 14 | 54 | 0.0198 | 3.92E-07 | ||
5 | 12 | 0.0353 | 7.29E-06 | 11 | 38 | 0.0340 | 7.19E-06 | 2 | 9 | 0.0136 | 0.00E+00 | ||
4 | 8 | 0.0247 | 1.69E-07 | 10 | 32 | 0.0334 | 8.33E-06 | 2 | 8 | 0.0197 | 0.00E+00 | ||
5 | 11 | 0.0330 | 1.28E-07 | 12 | 38 | 1.4578 | 1.70E-06 | 4 | 14 | 0.0172 | 2.22E-16 | ||
7 | 16 | 0.0494 | 1.79E-06 | 19 | 69 | 0.0617 | 2.22E-06 | 12 | 47 | 0.0369 | 9.52E-07 | ||
9 | 20 | 0.0565 | 2.04E-06 | 19 | 69 | 0.0724 | 2.22E-06 | 15 | 59 | 0.0548 | 3.37E-07 | ||
9 | 19 | 0.0677 | 4.92E-06 | 11 | 36 | 0.0424 | 3.32E-06 | 14 | 54 | 0.0385 | 6.25E-07 | ||
9 | 20 | 0.0583 | 2.04E-06 | 19 | 69 | 0.0908 | 2.22E-06 | 15 | 59 | 0.0642 | 3.32E-07 | ||
9 | 20 | 0.0440 | 2.04E-06 | 27 | 122 | 0.1471 | 3.72E-06 | 15 | 59 | 0.0605 | 3.36E-07 | ||
6 | 14 | 0.0693 | 3.67E-10 | 12 | 41 | 0.0766 | 4.72E-06 | 2 | 9 | 0.0312 | 0.00E+00 | ||
4 | 8 | 0.0665 | 2.39E-07 | 11 | 35 | 0.0800 | 1.49E-06 | 2 | 8 | 0.0131 | 0.00E+00 | ||
5 | 11 | 0.0537 | 1.28E-07 | 12 | 38 | 2.5950 | 1.70E-06 | 4 | 14 | 0.0239 | 2.22E-16 | ||
8 | 18 | 0.1273 | 3.07E-07 | 17 | 62 | 0.1395 | 9.13E-06 | 12 | 47 | 0.0824 | 7.20E-07 | ||
9 | 20 | 0.0858 | 2.89E-06 | 17 | 62 | 0.1122 | 9.13E-06 | 15 | 59 | 0.0614 | 4.78E-07 | ||
9 | 19 | 0.1316 | 4.92E-06 | 11 | 36 | 0.0749 | 3.32E-06 | 14 | 54 | 0.0617 | 7.36E-07 | ||
9 | 20 | 0.0844 | 2.89E-06 | 17 | 62 | 0.1038 | 9.13E-06 | 15 | 59 | 0.0613 | 4.75E-07 | ||
9 | 20 | 0.1005 | 2.89E-06 | 27 | 103 | 0.4661 | 2.52E-06 | 15 | 59 | 0.0524 | 4.75E-07 | ||
7 | 20 | 0.4618 | 3.27E-08 | 13 | 44 | 0.3079 | 7.07E-07 | 2 | 10 | 0.0474 | 0.00E+00 | ||
4 | 8 | 0.1123 | 5.35E-07 | 11 | 35 | 0.3012 | 3.33E-06 | 2 | 8 | 0.0923 | 0.00E+00 | ||
5 | 11 | 0.1031 | 1.28E-07 | 12 | 38 | 23.8270 | 1.70E-06 | 4 | 14 | 0.1142 | 2.22E-16 | ||
7 | 20 | 0.4022 | 3.43E-08 | 18 | 65 | 0.5567 | 8.62E-06 | 10 | 42 | 0.2322 | 7.89E-08 | ||
9 | 21 | 0.3592 | 4.85E-06 | 18 | 65 | 0.3972 | 8.62E-06 | 16 | 65 | 0.4585 | 8.55E-07 | ||
9 | 19 | 0.3959 | 4.92E-06 | 11 | 36 | 0.2964 | 3.32E-06 | f | f | f | f | ||
9 | 21 | 0.3742 | 4.85E-06 | 18 | 65 | 0.4319 | 8.62E-06 | 16 | 65 | 0.1987 | 8.49E-07 | ||
9 | 21 | 0.3703 | 4.85E-06 | 18 | 65 | 0.5524 | 8.97E-06 | 16 | 65 | 0.5407 | 8.39E-07 | ||
7 | 23 | 0.7369 | 4.77E-06 | 13 | 44 | 0.7618 | 1.00E-06 | 3 | 16 | 0.1932 | 0.00E+00 | ||
4 | 8 | 0.2658 | 7.57E-07 | 11 | 35 | 0.4434 | 4.71E-06 | 2 | 8 | 0.1158 | 0.00E+00 | ||
5 | 11 | 0.3353 | 1.28E-07 | 12 | 38 | 107.4606 | 1.70E-06 | 4 | 14 | 0.2615 | 2.22E-16 | ||
7 | 23 | 0.7591 | 4.81E-06 | 19 | 68 | 0.4613 | 2.35E-06 | 14 | 59 | 0.6242 | 5.49E-07 | ||
9 | 22 | 0.7743 | 8.65E-06 | 19 | 68 | 1.1533 | 2.35E-06 | f | f | f | f | ||
9 | 19 | 0.6254 | 4.92E-06 | 11 | 36 | 0.5491 | 3.32E-06 | f | f | f | f | ||
9 | 22 | 0.7055 | 8.65E-06 | 19 | 68 | 1.0239 | 2.35E-06 | f | f | f | f | ||
9 | 22 | 0.5172 | 8.66E-06 | 19 | 68 | 0.9601 | 2.41E-06 | f | f | f | f |
DPPM | MDYP | WYLP | |||||||||||
DIMENSION | INITIAL POINT | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM | ITER | FVAL | TIME | NORM |
1000 | 5 | 12 | 0.2244 | 3.26E-06 | 11 | 38 | 0.2095 | 3.21E-06 | 2 | 9 | 0.0260 | 0.00E+00 | |
4 | 8 | 0.1030 | 7.57E-08 | 9 | 29 | 0.0294 | 8.71E-06 | 2 | 8 | 0.0143 | 0.00E+00 | ||
5 | 11 | 0.0745 | 1.28E-07 | 12 | 38 | 0.1401 | 1.70E-06 | 4 | 14 | 0.0322 | 2.22E-16 | ||
7 | 16 | 0.0238 | 1.92E-06 | 21 | 79 | 0.0319 | 6.66E-06 | 12 | 45 | 0.0305 | 7.78E-08 | ||
9 | 19 | 0.0954 | 6.02E-06 | 21 | 79 | 0.0333 | 6.66E-06 | 14 | 54 | 0.0385 | 3.41E-07 | ||
9 | 19 | 0.0316 | 4.09E-06 | 11 | 36 | 0.0131 | 3.32E-06 | 14 | 54 | 0.0249 | 2.67E-07 | ||
9 | 19 | 0.0215 | 6.02E-06 | 21 | 79 | 0.0265 | 6.66E-06 | 14 | 54 | 0.0204 | 3.42E-07 | ||
9 | 19 | 0.0286 | 5.97E-06 | 17 | 61 | 0.0164 | 6.86E-06 | 14 | 54 | 0.0198 | 3.92E-07 | ||
5 | 12 | 0.0353 | 7.29E-06 | 11 | 38 | 0.0340 | 7.19E-06 | 2 | 9 | 0.0136 | 0.00E+00 | ||
4 | 8 | 0.0247 | 1.69E-07 | 10 | 32 | 0.0334 | 8.33E-06 | 2 | 8 | 0.0197 | 0.00E+00 | ||
5 | 11 | 0.0330 | 1.28E-07 | 12 | 38 | 1.4578 | 1.70E-06 | 4 | 14 | 0.0172 | 2.22E-16 | ||
7 | 16 | 0.0494 | 1.79E-06 | 19 | 69 | 0.0617 | 2.22E-06 | 12 | 47 | 0.0369 | 9.52E-07 | ||
9 | 20 | 0.0565 | 2.04E-06 | 19 | 69 | 0.0724 | 2.22E-06 | 15 | 59 | 0.0548 | 3.37E-07 | ||
9 | 19 | 0.0677 | 4.92E-06 | 11 | 36 | 0.0424 | 3.32E-06 | 14 | 54 | 0.0385 | 6.25E-07 | ||
9 | 20 | 0.0583 | 2.04E-06 | 19 | 69 | 0.0908 | 2.22E-06 | 15 | 59 | 0.0642 | 3.32E-07 | ||
9 | 20 | 0.0440 | 2.04E-06 | 27 | 122 | 0.1471 | 3.72E-06 | 15 | 59 | 0.0605 | 3.36E-07 | ||
6 | 14 | 0.0693 | 3.67E-10 | 12 | 41 | 0.0766 | 4.72E-06 | 2 | 9 | 0.0312 | 0.00E+00 | ||
4 | 8 | 0.0665 | 2.39E-07 | 11 | 35 | 0.0800 | 1.49E-06 | 2 | 8 | 0.0131 | 0.00E+00 | ||
5 | 11 | 0.0537 | 1.28E-07 | 12 | 38 | 2.5950 | 1.70E-06 | 4 | 14 | 0.0239 | 2.22E-16 | ||
8 | 18 | 0.1273 | 3.07E-07 | 17 | 62 | 0.1395 | 9.13E-06 | 12 | 47 | 0.0824 | 7.20E-07 | ||
9 | 20 | 0.0858 | 2.89E-06 | 17 | 62 | 0.1122 | 9.13E-06 | 15 | 59 | 0.0614 | 4.78E-07 | ||
9 | 19 | 0.1316 | 4.92E-06 | 11 | 36 | 0.0749 | 3.32E-06 | 14 | 54 | 0.0617 | 7.36E-07 | ||
9 | 20 | 0.0844 | 2.89E-06 | 17 | 62 | 0.1038 | 9.13E-06 | 15 | 59 | 0.0613 | 4.75E-07 | ||
9 | 20 | 0.1005 | 2.89E-06 | 27 | 103 | 0.4661 | 2.52E-06 | 15 | 59 | 0.0524 | 4.75E-07 | ||
7 | 20 | 0.4618 | 3.27E-08 | 13 | 44 | 0.3079 | 7.07E-07 | 2 | 10 | 0.0474 | 0.00E+00 | ||
4 | 8 | 0.1123 | 5.35E-07 | 11 | 35 | 0.3012 | 3.33E-06 | 2 | 8 | 0.0923 | 0.00E+00 | ||
5 | 11 | 0.1031 | 1.28E-07 | 12 | 38 | 23.8270 | 1.70E-06 | 4 | 14 | 0.1142 | 2.22E-16 | ||
7 | 20 | 0.4022 | 3.43E-08 | 18 | 65 | 0.5567 | 8.62E-06 | 10 | 42 | 0.2322 | 7.89E-08 | ||
9 | 21 | 0.3592 | 4.85E-06 | 18 | 65 | 0.3972 | 8.62E-06 | 16 | 65 | 0.4585 | 8.55E-07 | ||
9 | 19 | 0.3959 | 4.92E-06 | 11 | 36 | 0.2964 | 3.32E-06 | f | f | f | f | ||
9 | 21 | 0.3742 | 4.85E-06 | 18 | 65 | 0.4319 | 8.62E-06 | 16 | 65 | 0.1987 | 8.49E-07 | ||
9 | 21 | 0.3703 | 4.85E-06 | 18 | 65 | 0.5524 | 8.97E-06 | 16 | 65 | 0.5407 | 8.39E-07 | ||
7 | 23 | 0.7369 | 4.77E-06 | 13 | 44 | 0.7618 | 1.00E-06 | 3 | 16 | 0.1932 | 0.00E+00 | ||
4 | 8 | 0.2658 | 7.57E-07 | 11 | 35 | 0.4434 | 4.71E-06 | 2 | 8 | 0.1158 | 0.00E+00 | ||
5 | 11 | 0.3353 | 1.28E-07 | 12 | 38 | 107.4606 | 1.70E-06 | 4 | 14 | 0.2615 | 2.22E-16 | ||
7 | 23 | 0.7591 | 4.81E-06 | 19 | 68 | 0.4613 | 2.35E-06 | 14 | 59 | 0.6242 | 5.49E-07 | ||
9 | 22 | 0.7743 | 8.65E-06 | 19 | 68 | 1.1533 | 2.35E-06 | f | f | f | f | ||
9 | 19 | 0.6254 | 4.92E-06 | 11 | 36 | 0.5491 | 3.32E-06 | f | f | f | f | ||
9 | 22 | 0.7055 | 8.65E-06 | 19 | 68 | 1.0239 | 2.35E-06 | f | f | f | f | ||
9 | 22 | 0.5172 | 8.66E-06 | 19 | 68 | 0.9601 | 2.41E-06 | f | f | f | f |
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