Mesh-based Nelder–Mead algorithm for inequality constrained optimization

被引：0
作者：
Charles Audet
Christophe Tribes
机构：
[1] École Polytechnique de Montréal,GERAD and Département de Mathématiques et Génie Industriel
来源：
Computational Optimization and Applications | 2018年 / 71卷
关键词：
Nelder–Mead; MADS; Derivative-free optimization; Blackbox optimization; Constrained optimization;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Despite the lack of theoretical and practical convergence support, the Nelder–Mead (NM) algorithm is widely used to solve unconstrained optimization problems. It is a derivative-free algorithm, that attempts iteratively to replace the worst point of a simplex by a better one. The present paper proposes a way to extend the NM algorithm to inequality constrained optimization. This is done through a search step of the mesh adaptive direct search (Mads) algorithm, inspired by the NM algorithm. The proposed algorithm does not suffer from the NM lack of convergence, but instead inherits from the totality of the Mads convergence analysis. Numerical experiments show an important improvement in the quality of the solutions produced using this search step.
引用
收藏
页码：331 / 352
页数：21
相关论文
共 89 条
  • [11] Audet C(2010)Optimization of short-time gasoline blending scheduling problem with a DNA based hybrid genetic algorithm Chem. Eng. Process. 49 1076-1083
  • [12] Ianni A(2013)Use of quadratic models with mesh-adaptive direct search for constrained black box optimization Optim. Methods Softw. 28 139-158
  • [13] Le Digabel S(2000)Frame-based methods for unconstrained optimization J. Optim. Theory Appl. 107 261-274
  • [14] Tribes C(2002)Nonlinear programming without a penalty function Math. Program. Ser. A 91 239-269
  • [15] Audet C(2002)On the global convergence of a filter-SQP algorithm SIAM J. Optim. 13 44-59
  • [16] Kokkolaras M(2012)Implementing the Nelder–Mead simplex algorithm with adaptive parameters Comput. Optim. Appl. 51 259-277
  • [17] Le Digabel S(2003)CUTEr (and SifDec): a constrained and unconstrained testing environment, revisited ACM Trans. Math. Softw. 29 373-394
  • [18] Talgorn B(2013)A literature survey of benchmark functions for global optimisation problems Int. J. Math. Modell. Numer. Optim. 4 150-194
  • [19] Audet C(1999)Detection and remediation of stagnation in the Nelder–Mead algorithm using a sufficient decrease condition SIAM J. Optim. 10 43-55
  • [20] Le Digabel S(2011)Sequential approximate optimization using radial basis function network for engineering optimization Optim. Eng. 12 535-557
123456789