Direct search algorithm for bilevel programming problems

被引：20

作者：

Mersha, Ayalew Getachew ^{[1
]}

Dempe, Stephan ^{[1
]}

机构：

[1] Tech Univ Bergakad Freiberg, Dept Math & Comp Sci, D-09596 Freiberg, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2011年 / 49卷 / 01期

关键词：

Bilevel programming; Nonsmooth optimization; Solution algorithm; Direct search algorithm; Clarke stationary solution; ADAPTIVE DIRECT SEARCH; CONVERGENCE;

D O I：

10.1007/s10589-009-9295-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we study the application of a class of direct search methods to bilevel programming with convex lower level problems with strongly stable optimal solutions. In those methods, directions of descent in each iterations are selected within a finite set of directions. To guarantee the existence of such a finite set, we investigate the relation between the aperture of a descent cone at a non stationary point and the vector density of a finite set of directions. It is shown that the direct search method converges to a Clarke stationary point of the bilevel programming problem.

引用

页码：1 / 15

页数：15

共 50 条

[31] Discrete differential evolution algorithm for integer linear bilevel programming problems
Li, Hong
Zhang, Li
Jiao, Yongchang
[J]. JOURNAL OF SYSTEMS ENGINEERING AND ELECTRONICS, 2016, 27 (04) : 912 - 919
[32] A genetic algorithm for solving a special class of Nonlinear bilevel programming problems
Li, Hecheng
Wang, Yuping
[J]. COMPUTATIONAL SCIENCE - ICCS 2007, PT 4, PROCEEDINGS, 2007, 4490 : 1159 - +
[33] Co-evolutionary algorithm: An efficient approach for bilevel programming problems
Li, Hecheng
Fang, Lei
[J]. ENGINEERING OPTIMIZATION, 2014, 46 (03) : 361 - 376
[34] IMPROVED DIRECT SEARCH MATHEMATICAL PROGRAMMING ALGORITHM
PAPPAS, M
MORADI, JY
[J]. MECHANICAL ENGINEERING, 1975, 97 (12): : 97 - 97
[35] IMPROVED DIRECT SEARCH MATHEMATICAL PROGRAMMING ALGORITHM
PAPPAS, M
MORADI, JY
[J]. JOURNAL OF ENGINEERING FOR INDUSTRY-TRANSACTIONS OF THE ASME, 1975, 97 (04): : 1305 - 1310
[36] A hybrid intelligent algorithm by combining particle swarm optimization with variable neighborhood search for solving nonlinear bilevel programming problems
School of Air and Missile Defense, Air force Engineering University, Xi'an
710051, China
[J]. Xitong Gongcheng Lilum yu Shijian, 2 (473-480):
[37] Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm
Jean Bosco Etoa Etoa
[J]. Journal of Global Optimization, 2010, 47 : 615 - 637
[38] Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm
Etoa, Jean Bosco Etoa
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2010, 47 (04) : 615 - 637
[39] A Hybrid Evolutionary Algorithm for Mixed-Integer Nonlinear Bilevel Programming Problems
Li, Hong
Jiao, Yong-Chang
[J]. SECOND INTERNATIONAL CONFERENCE ON GENETIC AND EVOLUTIONARY COMPUTING: WGEC 2008, PROCEEDINGS, 2008, : 549 - +
[40] Multi-Sine Cosine Algorithm for Solving Nonlinear Bilevel Programming Problems
Yousria Abo-Elnaga
M. A. El-Shorbagy
[J]. International Journal of Computational Intelligence Systems, 2020, 13 : 421 - 432

← 1 2 3 4 5 →