Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization

被引：0
作者：
A. M. Bagirov
B. Karasözen
M. Sezer
机构：
[1] University of Ballarat,Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences
[2] Middle East Technical University,Department of Mathematics & Institute of Applied Mathematics
[3] Middle East Technical University,Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2008年 / 137卷
关键词：
Nonsmooth optimization; Derivative-free optimization; Subdifferentials; Discrete gradients;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.
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页码：317 / 334
页数：17
相关论文
共 24 条
  • [1] Frangioni A.(2002)Generalized bundle methods SIAM J. Optim. 113 117-156
  • [2] Gaudioso M.(1982)A bundle type approach to the unconstrained minimization of convex nonsmooth functions Math. Program. 23 216-226
  • [3] Monaco M.F.(1977)An algorithm for constrained optimization with semismooth functions Math. Oper. Res. 2 191-207
  • [4] Mifflin R.(1975)A method of conjugate subgradients of minimizing nondifferentiable convex functions Math. Program. Study 3 145-173
  • [5] Wolfe P.H.(2003)Algorithms for finite and semi-infinite min-max-min problems using adaptive smoothing techniques J. Optim. Theory Appl. 119 421-457
  • [6] Polak E.(2005)A robust gradient sampling algorithm for nonsmooth, nonconvex optimization SIAM J. Optim. 15 751-779
  • [7] Royset J.O.(2003)Analysis of generalized pattern searches SIAM J. Optim. 13 889-903
  • [8] Burke J.V.(1997)On the convergence of pattern search algorithms SIAM J. Optim. 7 1-25
  • [9] Lewis A.S.(1977)Semismooth and semiconvex functions in constrained optimization SIAM J. Control Optim. 15 959-972
  • [10] Overton M.L.(2003)Supervised and unsupervised data classification via nonsmooth and global optimisation TOP: Spanish Oper. Res. J. 11 1-93
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