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
收藏
页码：1 / 15
页数：15
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