Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

被引：15

作者：

Chadli, Ouayl ^{[1
]}

Ansari, Qamrul Hasan ^{[2
,3
]}

Al-Homidan, Suliman ^{[3
]}

机构：

[1] Ibn Zohr Univ, Fac Econ & Social Sci, Dept Econ, BP 8658 Poste Dakhla, Agadir, Morocco

[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[3] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran, Saudi Arabia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2017年 / 172卷 / 03期

关键词：

Bilevel vector equilibrium problems; Mixed vector equilibrium problems; Vector equilibrium problems; Bilevel programs; Auxiliary principle; C-maximal bifunctions; C-monotone bifunctions; C-convex functions; C-upper (lower) semicontinuity; Convergence analysis; MATHEMATICAL PROGRAMS; PENALTY;

D O I：

10.1007/s10957-017-1062-y

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：

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.

引用

页码：726 / 758

页数：33

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