
Previous Article
A nonconvergent example for the iterative waterfilling algorithm
 NACO Home
 This Issue

Next Article
Filterbased genetic algorithm for mixed variable programming
A derivativefree trustregion algorithm for unconstrained optimization with controlled error
1.  Graduate School of Informatics, Kyoto University, Yoshidahonmachi, Sakyoku, Kyoto, 6068501,, Japan 
2.  Graduate School of Informatics, Kyoto University, Yoshidahonmachi, Sakyoku, Kyoto, 6068501 
References:
[1] 
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing environment, ACM Transactions on Mathematical Software, 21 (1995), 123160. doi: 10.1145/200979.201043. 
[2] 
A. J. Booker, J. E. Dennis, P. D. Frank, D. B. Serafini, V. Torczon and M. W. Trosset, A rigorous framework for optimization of expensive functions by surrogates, Structural and Multidisciplinary Optimization, 17 (1999), 113. 
[3] 
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering, SIAM Journal on Optimization, 10 (2000), 11491162. doi: 10.1137/S1052623499354096. 
[4] 
B. Colson, P. Marcotte and G. Savard, Bilevel programming: A survey, 4OR: A Quarterly Journal of Operations Research, 3 (2005), 87107. 
[5] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods,'' SIAM, Philadelphia, 2000. doi: 10.1137/1.9780898719857. 
[6] 
A. R. Conn and Ph. L. Toint, An algorithm using quadratic interpolation for unconstrained derivative free optimization, in "Nonlinear Optimization and Applications,'' Plenum Publishing, (1996), 2747. 
[7] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization algorithm in practice, the American Institute of Aeronautics and Astronautics Conference, St Louis, 1998. 
[8] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization method via support vector machines,, 1999. Available from: , (). 
[9] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, On the convergence of derivativefree methods for unconstrained optimization, in "Approximation Theory and Optimization,'' Cambridge University Press, (1997), 83108. 
[10] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization, Mathematical Programming, 111 (2008), 141172. doi: 10.1007/s1010700600735. 
[11] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation, IMA Journal of Numerical Analysis, 28 (2008), 721748. doi: 10.1093/imanum/drn046. 
[12] 
C. Cox and M. Rubinstein, "Option Markets,'' PrenticeHall, 1985. 
[13] 
N. Cristianini and J. ShaweTaylor, "An Introduction to Support Vector Machines and Other Kernelbased Methods,'' Cambridge University Press, Cambridge, UK, 2000. 
[14] 
J. E. Dennis and V. Torczon, Direct search methods on parallel machines, SIAM Journal on Optimization, 1 (1991), 448474. doi: 10.1137/0801027. 
[15] 
R. A. Fisher, "The Design of Experiments,'' Oliver and Boyd Ltd., 1951. 
[16] 
P. Gilmore and C. T. Kelley, An implicit filtering algorithm for optimization of functions with many local minima, SIAM Journal on Optimization, 5 (1995), 269285. doi: 10.1137/0805015. 
[17] 
B. Karasözen, Survey of trustregion derivative free optimization methods, Journal of Industrial and Management Optimization, 3 (2007), 321334. 
[18] 
T. G. Kolda, R. M. Lewis and V. Torzcon, Optimization by direct search: new perspectives of some classical and modern methods, SIAM Review, 45 (2003), 385482. doi: 10.1137/S003614450242889. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[20] 
J. Nocedal and S. J. Wright, "Numerical Optimization,'' SpringerVerlag, New York, 1999. doi: 10.1007/b98874. 
[21] 
M. J. D. Powell, Trust region methods that employ quadratic interpolation to the objective function, Presentation at the 5th SIAM Conference on Optimization, 1996. 
[22] 
M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation, Mathematical Programming, 92 (2002), 555582. doi: 10.1007/s101070100290. 
[23] 
J. A. Tilley, Valuing American options in a path simulation model, Transactions of the Society of Actuaries, 45 (1993), 83104. 
[24] 
V. Torczon, On the convergence of the multidirectional search algorithm, SIAM Journal on Optimization, 1 (1991), 123145. doi: 10.1137/0801010. 
[25] 
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'' PhD thesis, Harvard University in Cambridge, 1969. 
[26] 
D. Winfield, Functional minimization by interpolation in a data table, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339347. doi: 10.1093/imamat/12.3.339. 
show all references
References:
[1] 
I. Bongartz, A. R. Conn, N. I. M. Gould and Ph. L. Toint, CUTE: Constrained and unconstrained testing environment, ACM Transactions on Mathematical Software, 21 (1995), 123160. doi: 10.1145/200979.201043. 
[2] 
A. J. Booker, J. E. Dennis, P. D. Frank, D. B. Serafini, V. Torczon and M. W. Trosset, A rigorous framework for optimization of expensive functions by surrogates, Structural and Multidisciplinary Optimization, 17 (1999), 113. 
[3] 
T. D. Choi and C. T. Kelley, Superlinear Convergence and Implicit Filtering, SIAM Journal on Optimization, 10 (2000), 11491162. doi: 10.1137/S1052623499354096. 
[4] 
B. Colson, P. Marcotte and G. Savard, Bilevel programming: A survey, 4OR: A Quarterly Journal of Operations Research, 3 (2005), 87107. 
[5] 
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "TrustRegion Methods,'' SIAM, Philadelphia, 2000. doi: 10.1137/1.9780898719857. 
[6] 
A. R. Conn and Ph. L. Toint, An algorithm using quadratic interpolation for unconstrained derivative free optimization, in "Nonlinear Optimization and Applications,'' Plenum Publishing, (1996), 2747. 
[7] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization algorithm in practice, the American Institute of Aeronautics and Astronautics Conference, St Louis, 1998. 
[8] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, A derivative free optimization method via support vector machines,, 1999. Available from: , (). 
[9] 
A. R. Conn, K. Scheinberg and Ph. L. Toint, On the convergence of derivativefree methods for unconstrained optimization, in "Approximation Theory and Optimization,'' Cambridge University Press, (1997), 83108. 
[10] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of interpolation sets in derivative free optimization, Mathematical Programming, 111 (2008), 141172. doi: 10.1007/s1010700600735. 
[11] 
A. R. Conn, K. Scheinberg and L. N. Vicente, Geometry of sample sets in derivative free optimization: Polynomial regression and underdetermined interpolation, IMA Journal of Numerical Analysis, 28 (2008), 721748. doi: 10.1093/imanum/drn046. 
[12] 
C. Cox and M. Rubinstein, "Option Markets,'' PrenticeHall, 1985. 
[13] 
N. Cristianini and J. ShaweTaylor, "An Introduction to Support Vector Machines and Other Kernelbased Methods,'' Cambridge University Press, Cambridge, UK, 2000. 
[14] 
J. E. Dennis and V. Torczon, Direct search methods on parallel machines, SIAM Journal on Optimization, 1 (1991), 448474. doi: 10.1137/0801027. 
[15] 
R. A. Fisher, "The Design of Experiments,'' Oliver and Boyd Ltd., 1951. 
[16] 
P. Gilmore and C. T. Kelley, An implicit filtering algorithm for optimization of functions with many local minima, SIAM Journal on Optimization, 5 (1995), 269285. doi: 10.1137/0805015. 
[17] 
B. Karasözen, Survey of trustregion derivative free optimization methods, Journal of Industrial and Management Optimization, 3 (2007), 321334. 
[18] 
T. G. Kolda, R. M. Lewis and V. Torzcon, Optimization by direct search: new perspectives of some classical and modern methods, SIAM Review, 45 (2003), 385482. doi: 10.1137/S003614450242889. 
[19] 
J. A. Nelder and R. Mead, A simplex method for function minimization, Computer Journal, 7 (1965), 308313. 
[20] 
J. Nocedal and S. J. Wright, "Numerical Optimization,'' SpringerVerlag, New York, 1999. doi: 10.1007/b98874. 
[21] 
M. J. D. Powell, Trust region methods that employ quadratic interpolation to the objective function, Presentation at the 5th SIAM Conference on Optimization, 1996. 
[22] 
M. J. D. Powell, UOBYQA: unconstrained optimization by quadratic approximation, Mathematical Programming, 92 (2002), 555582. doi: 10.1007/s101070100290. 
[23] 
J. A. Tilley, Valuing American options in a path simulation model, Transactions of the Society of Actuaries, 45 (1993), 83104. 
[24] 
V. Torczon, On the convergence of the multidirectional search algorithm, SIAM Journal on Optimization, 1 (1991), 123145. doi: 10.1137/0801010. 
[25] 
D. Winfield, "Function and Functional Optimization by Interpolation in Data Tables,'' PhD thesis, Harvard University in Cambridge, 1969. 
[26] 
D. Winfield, Functional minimization by interpolation in a data table, Journal of the Institute of Mathematics and its Applications, 12 (1973), 339347. doi: 10.1093/imamat/12.3.339. 
[1] 
Liang Zhang, Wenyu Sun, Raimundo J. B. de Sampaio, Jinyun Yuan. A wedge trust region method with selfcorrecting geometry for derivativefree optimization. Numerical Algebra, Control and Optimization, 2015, 5 (2) : 169184. doi: 10.3934/naco.2015.5.169 
[2] 
Bülent Karasözen. Survey of trustregion derivative free optimization methods. Journal of Industrial and Management Optimization, 2007, 3 (2) : 321334. doi: 10.3934/jimo.2007.3.321 
[3] 
A. M. Bagirov, Moumita Ghosh, Dean Webb. A derivativefree method for linearly constrained nonsmooth optimization. Journal of Industrial and Management Optimization, 2006, 2 (3) : 319338. doi: 10.3934/jimo.2006.2.319 
[4] 
WeiZhe Gu, LiYong Lu. The linear convergence of a derivativefree descent method for nonlinear complementarity problems. Journal of Industrial and Management Optimization, 2017, 13 (2) : 531548. doi: 10.3934/jimo.2016030 
[5] 
Min Xi, Wenyu Sun, Jun Chen. Survey of derivativefree optimization. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 537555. doi: 10.3934/naco.2020050 
[6] 
Jirui Ma, Jinyan Fan. On convergence properties of the modified trust region method under Hölderian error bound condition. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021222 
[7] 
Yannan Chen, Jingya Chang. A trust region algorithm for computing extreme eigenvalues of tensors. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 475485. doi: 10.3934/naco.2020046 
[8] 
Gaohang Yu. A derivativefree method for solving largescale nonlinear systems of equations. Journal of Industrial and Management Optimization, 2010, 6 (1) : 149160. doi: 10.3934/jimo.2010.6.149 
[9] 
DongHui Li, XiaoLin Wang. A modified FletcherReevesType derivativefree method for symmetric nonlinear equations. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 7182. doi: 10.3934/naco.2011.1.71 
[10] 
Yigui Ou, Wenjie Xu. A unified derivativefree projection method model for largescale nonlinear equations with convex constraints. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021125 
[11] 
Nobuko Sagara, Masao Fukushima. trust region method for nonsmooth convex optimization. Journal of Industrial and Management Optimization, 2005, 1 (2) : 171180. doi: 10.3934/jimo.2005.1.171 
[12] 
Xin Zhang, Jie Wen, Qin Ni. Subspace trustregion algorithm with conic model for unconstrained optimization. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 223234. doi: 10.3934/naco.2013.3.223 
[13] 
Honglan Zhu, Qin Ni, Meilan Zeng. A quasiNewton trust region method based on a new fractional model. Numerical Algebra, Control and Optimization, 2015, 5 (3) : 237249. doi: 10.3934/naco.2015.5.237 
[14] 
Jun Chen, Wenyu Sun, Zhenghao Yang. A nonmonotone retrospective trustregion method for unconstrained optimization. Journal of Industrial and Management Optimization, 2013, 9 (4) : 919944. doi: 10.3934/jimo.2013.9.919 
[15] 
Lijuan Zhao, Wenyu Sun. Nonmonotone retrospective conic trust region method for unconstrained optimization. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 309325. doi: 10.3934/naco.2013.3.309 
[16] 
Dan Xue, Wenyu Sun, Hongjin He. A structured trust region method for nonconvex programming with separable structure. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 283293. doi: 10.3934/naco.2013.3.283 
[17] 
Zhou Sheng, Gonglin Yuan, Zengru Cui, Xiabin Duan, Xiaoliang Wang. An adaptive trust region algorithm for largeresidual nonsmooth least squares problems. Journal of Industrial and Management Optimization, 2018, 14 (2) : 707718. doi: 10.3934/jimo.2017070 
[18] 
Chunlin Hao, Xinwei Liu. A trustregion filterSQP method for mathematical programs with linear complementarity constraints. Journal of Industrial and Management Optimization, 2011, 7 (4) : 10411055. doi: 10.3934/jimo.2011.7.1041 
[19] 
Jing Zhou, Cheng Lu, Ye Tian, Xiaoying Tang. A SOCP relaxation based branchandbound method for generalized trustregion subproblem. Journal of Industrial and Management Optimization, 2021, 17 (1) : 151168. doi: 10.3934/jimo.2019104 
[20] 
Hatim Tayeq, Amal Bergam, Anouar El Harrak, Kenza Khomsi. Selfadaptive algorithm based on a posteriori analysis of the error applied to air quality forecasting using the finite volume method. Discrete and Continuous Dynamical Systems  S, 2021, 14 (7) : 25572570. doi: 10.3934/dcdss.2020400 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]