GENERALIZED PROXIMAL DISTANCES FOR BILEVEL EQUILIBRIUM PROBLEMS

被引：21

作者：

Bento, G. C. ^{[1
]}

Cruz Neto, J. X. ^{[2
]}

Lopes, J. O. ^{[2
]}

Soares, P. A., Jr. ^{[2
]}

Soubeyran, A. ^{[3
,4
,5
]}

机构：

[1] Univ Fed Goias, IME, BR-74001970 Goiania, Go, Brazil

[2] Univ Fed Piaui, DM, CCN, BR-64049550 Teresina, PI, Brazil

[3] Aix Marseille Univ, Aix Marseille Sch Econ, Marseille, France

[4] CNRS, F-75700 Paris, France

[5] EHESS, Paris, France

来源：

SIAM JOURNAL ON OPTIMIZATION | 2016年 / 26卷 / 01期

关键词：

equilibrium problem; bilevel problem; proximal algorithms; proximal distance; variational rationality; OPTIMIZATION PROBLEMS; CONVEX; CONVERGENCE; ALGORITHMS;

D O I：

10.1137/140975589

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequence generated by the algorithm. This class of problems is very interesting because it covers mathematical programs and optimization problems under equilibrium constraints. As an application, we consider the problem of the stability and change dynamics of a leader-follower relationship in a hierarchical organization.

引用

页码：810 / 830

页数：21

共 39 条

[1] Well-Posedness Under Relaxed Semicontinuity for Bilevel Equilibrium and Optimization Problems with Equilibrium Constraints [J].