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Solution properties and error bounds for semi-infinite complementarity problems
Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints
1. | Jiangxi Key Laboratory of Numerical Simulation Technology, School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000 |
2. | School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, 341000, China |
3. | School of Biomedical Engineering, Southern Medical University, Guangzhou, 510515, China |
References:
[1] |
J. Barzilai and J. M. Borwein, Two point step size gradient methods, IMA J. Numer. Anal., 8 (1988), 141-148.
doi: 10.1093/imanum/8.1.141. |
[2] |
S. P. Dirkse and M. C. Ferris, MCPLIB: A collection of nonlinear mixed complementarity problems, Optim. Meth. Soft., 5 (1995), 319-345.
doi: 10.1080/10556789508805619. |
[3] |
E. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program. Ser. A, 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[4] |
M. E. El-Hawary, "Optimal Power Flow: Solution Techniques, Requirement and Challenges," IEEE Service Center, Piscataway, 1996. |
[5] |
L. Han, G. H. Yu and L. T. Guan, Multivariate spectral gradient method for unconstrained optimization, Appl. Math. and Comput., 201 (2008), 621-630.
doi: 10.1016/j.amc.2007.12.054. |
[6] |
A. N. Iusem and M. V. Solodov, Newton-type methods with generalized distances for constrained optimization, Optim., 41 (1997), 257-278.
doi: 10.1080/02331939708844339. |
[7] |
W. La Cruz, J. M. Martinez 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. |
[8] |
W. La Cruz and M. Raydan, Nonmonotone spectral methods for large-scale nonlinear systems, Optim. Meth. Soft., 18 (2003), 583-599.
doi: 10.1080/10556780310001610493. |
[9] |
D. H. Li and X. L. Wang, A modified Fletcher-Reeves-type derivative-free method for symmetric nonlinear equations, Numer. Alge. Ctrl. Optim., 1 (2011), 71-82. |
[10] |
Q. N. 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. |
[11] |
F. M. Ma and C. W. Wang, Modified projection method for solving a system of monotone equations with convex constraints, Appl. Math. Comput., 34 (2010), 47-56. |
[12] |
K. Meintjes and A. P. Morgan, A methodology for solving chemical equilibrium systems, Appl. Math. Comput., 22 (1987), 333-361.
doi: 10.1016/0096-3003(87)90076-2. |
[13] |
K. Meintjes and A. P. Morgan, Chemical equilibrium systems as numerical test problems, ACM Trans. Math. Soft., 16 (1990), 143-151.
doi: 10.1145/78928.78930. |
[14] |
J. M. Ortega and W. C. Rheinboldt, "Iterative Solution of Nonlinear Equations in Several Variables," Academic Press, New York, 1970. |
[15] |
M. V. Solodov and B. F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in "Reformulation: Nonsmooth, Piecewise smooth, Semismooth and Smooth Methods" (eds. M. Fukushima and L. Qi), Kluwer Academic Publishers, (1998), 355-369. |
[16] |
C. W. Wang, Y. J. Wang and C. L. Xu, A projection method for a system of nonlinear monotone equations with convex constraints, Math. Meth. Oper. Res., 66 (2007), 33-46.
doi: 10.1007/s00186-006-0140-y. |
[17] |
A. J. Wood and B. F. Wollenberg, "Power Generations, Operations and Control," Wiley, New York, 1996. |
[18] |
N. Yamashita and M. Fukushima, Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems, Math. Program., 76 (1997), 469-491, (2000), 583-599. |
[19] |
G. H. Yu, A derivative-free method for solving large-scale nonlinear systems of equations, J. Ind. Manag. Optim., 6 (2010), 149-160.
doi: 10.3934/jimo.2010.6.149. |
[20] |
G. H. Yu, Nonmonotone spectral gradient-type methods for large-scaleunconstrained optimization and nonlinear systems of equations, Pacific J. Optim., 7 (2011), 387-404. |
[21] |
Z. S. Yu, J. Lin, J. Sun, Y. H. Xiao, L. Y. 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. |
[22] |
E. Zeidler, "Nonlinear Functional Analysis and Its Applications, II/B: Nonlinear Monotone Operators," Springer-Verlag, 1990.
doi: 10.1007/978-1-4612-0985-0. |
[23] |
L. Zhang and W. J. Zhou, Spectral gradient projection method for solving nonlinear monotone equations, J. Comput. Appl. Math., 196 (2006), 478-484.
doi: 10.1016/j.cam.2005.10.002. |
[24] |
W. J. Zhou and D. H. Li, Limited memory BFGS method for nonlinear monotone equations, J. Comp. Math., 25 (2007), 89-96. |
[25] |
W. J. Zhou and D. H. Li, A globally convergent BFGS method for nonlinear monotone equations without any merit functions, Math. Comp., 77 (2008), 2231-2240.
doi: 10.1090/S0025-5718-08-02121-2. |
show all references
References:
[1] |
J. Barzilai and J. M. Borwein, Two point step size gradient methods, IMA J. Numer. Anal., 8 (1988), 141-148.
doi: 10.1093/imanum/8.1.141. |
[2] |
S. P. Dirkse and M. C. Ferris, MCPLIB: A collection of nonlinear mixed complementarity problems, Optim. Meth. Soft., 5 (1995), 319-345.
doi: 10.1080/10556789508805619. |
[3] |
E. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program. Ser. A, 91 (2002), 201-213.
doi: 10.1007/s101070100263. |
[4] |
M. E. El-Hawary, "Optimal Power Flow: Solution Techniques, Requirement and Challenges," IEEE Service Center, Piscataway, 1996. |
[5] |
L. Han, G. H. Yu and L. T. Guan, Multivariate spectral gradient method for unconstrained optimization, Appl. Math. and Comput., 201 (2008), 621-630.
doi: 10.1016/j.amc.2007.12.054. |
[6] |
A. N. Iusem and M. V. Solodov, Newton-type methods with generalized distances for constrained optimization, Optim., 41 (1997), 257-278.
doi: 10.1080/02331939708844339. |
[7] |
W. La Cruz, J. M. Martinez 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. |
[8] |
W. La Cruz and M. Raydan, Nonmonotone spectral methods for large-scale nonlinear systems, Optim. Meth. Soft., 18 (2003), 583-599.
doi: 10.1080/10556780310001610493. |
[9] |
D. H. Li and X. L. Wang, A modified Fletcher-Reeves-type derivative-free method for symmetric nonlinear equations, Numer. Alge. Ctrl. Optim., 1 (2011), 71-82. |
[10] |
Q. N. 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. |
[11] |
F. M. Ma and C. W. Wang, Modified projection method for solving a system of monotone equations with convex constraints, Appl. Math. Comput., 34 (2010), 47-56. |
[12] |
K. Meintjes and A. P. Morgan, A methodology for solving chemical equilibrium systems, Appl. Math. Comput., 22 (1987), 333-361.
doi: 10.1016/0096-3003(87)90076-2. |
[13] |
K. Meintjes and A. P. Morgan, Chemical equilibrium systems as numerical test problems, ACM Trans. Math. Soft., 16 (1990), 143-151.
doi: 10.1145/78928.78930. |
[14] |
J. M. Ortega and W. C. Rheinboldt, "Iterative Solution of Nonlinear Equations in Several Variables," Academic Press, New York, 1970. |
[15] |
M. V. Solodov and B. F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in "Reformulation: Nonsmooth, Piecewise smooth, Semismooth and Smooth Methods" (eds. M. Fukushima and L. Qi), Kluwer Academic Publishers, (1998), 355-369. |
[16] |
C. W. Wang, Y. J. Wang and C. L. Xu, A projection method for a system of nonlinear monotone equations with convex constraints, Math. Meth. Oper. Res., 66 (2007), 33-46.
doi: 10.1007/s00186-006-0140-y. |
[17] |
A. J. Wood and B. F. Wollenberg, "Power Generations, Operations and Control," Wiley, New York, 1996. |
[18] |
N. Yamashita and M. Fukushima, Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems, Math. Program., 76 (1997), 469-491, (2000), 583-599. |
[19] |
G. H. Yu, A derivative-free method for solving large-scale nonlinear systems of equations, J. Ind. Manag. Optim., 6 (2010), 149-160.
doi: 10.3934/jimo.2010.6.149. |
[20] |
G. H. Yu, Nonmonotone spectral gradient-type methods for large-scaleunconstrained optimization and nonlinear systems of equations, Pacific J. Optim., 7 (2011), 387-404. |
[21] |
Z. S. Yu, J. Lin, J. Sun, Y. H. Xiao, L. Y. 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. |
[22] |
E. Zeidler, "Nonlinear Functional Analysis and Its Applications, II/B: Nonlinear Monotone Operators," Springer-Verlag, 1990.
doi: 10.1007/978-1-4612-0985-0. |
[23] |
L. Zhang and W. J. Zhou, Spectral gradient projection method for solving nonlinear monotone equations, J. Comput. Appl. Math., 196 (2006), 478-484.
doi: 10.1016/j.cam.2005.10.002. |
[24] |
W. J. Zhou and D. H. Li, Limited memory BFGS method for nonlinear monotone equations, J. Comp. Math., 25 (2007), 89-96. |
[25] |
W. J. Zhou and D. H. Li, A globally convergent BFGS method for nonlinear monotone equations without any merit functions, Math. Comp., 77 (2008), 2231-2240.
doi: 10.1090/S0025-5718-08-02121-2. |
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