STABILITY AND EXISTENCE OF SOLUTIONS FOR WEAK BILEVEL OPTIMIZATION PROBLEMS

被引：0

作者：

Keraoui H. ^{[1
]}

Saissi F.E. ^{[2
]}

Aboussoror A. ^{[1
]}

机构：

[1] Faculté des Sciences Semlalia, Cadi Ayyad University, Marrakech

[2] Laboratoire Analyse et Modélisation des Systèmes et Aide à la Décision, Ecole Nationale des Sciences Appliquées de Berrechid, Hassan Premier University, Berrechid

来源：

Applied Set-Valued Analysis and Optimization | 2024年 / 6卷 / 02期

关键词：

Bilevel optimization; Multifunctions; Stability analysis; Variational convergence;

D O I：

10.23952/asvao.6.2024.2.04

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). © 2024 Biemdas Academic Publishers. All rights reserved.

引用

页码：179 / 192

页数：13

共 50 条

[11] Existence of weak efficient solutions of set-valued optimization problems
Fakhar, Fatemeh
Hajisharifi, Hamid Reza
Soltani, Zeinab
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2024,
[12] EXISTENCE OF SOLUTIONS OF BILEVEL STRONG VECTOR EQUILIBRIUM PROBLEMS AND THEIR APPLICATIONS
Capata, Adela
[J]. JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2021, 5 (03): : 371 - 389
[13] Existence of solutions on weak vector equilibrium problems
Huang Longguang
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 65 (04) : 795 - 801
[14] EXISTENCE OF SOLUTIONS AND WELL-POSEDNESS FOR BILEVEL VECTOR EQUILIBRIUM PROBLEMS
Chen, Jiawei
Ju, Xingxing
Liou, Yeong-Cheng
Wen, Ching-Feng
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2018, 19 (12) : 2203 - 2217
[15] On the Existence of Solutions of Two Optimization Problems
Arabyan, Mariam
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 177 (02) : 291 - 305
[16] EXISTENCE OF SOLUTIONS TO A CLASS OF OPTIMIZATION PROBLEMS
CAMPOS, AS
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1973, AC18 (04) : 407 - 409
[17] Existence of Solutions in Vector Optimization Problems
I. V. Sergienko
T. T. Lebedeva
N. V. Semenova
[J]. Cybernetics and Systems Analysis, 2000, 36 : 823 - 828
[18] Existence of solutions for vector optimization problems
Lee, GM
Kim, DS
Kuk, H
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 220 (01) : 90 - 98
[19] Existence of solutions of optimization problems and porosity
Zaslavski, AJ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (02) : 1137 - 1147
[20] On existence of solutions in problems of vector optimization
Sergienko, I.V.
Lebedeva, T.T.
Semenova, N.V.
[J]. 2000, Naukova dumka

← 1 2 3 4 5 →