Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

Zai-Yun Peng, Jing-Jing Wang (), Xian-Jun Long () and Fu-Ping Liu ()
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Zai-Yun Peng: College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, P. R. China
Jing-Jing Wang: College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, P. R. China
Xian-Jun Long: College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China
Fu-Ping Liu: School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-22

Abstract: This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)n via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)n are obtained through a new nonlinear scalarization technical. Then, under ΓC-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)n is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)n under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

Keywords: Perturbed symmetric set-valued quasi-equilibrium problem; improvement sets; nonlinear scalarization; Painlevé–Kuratowski convergence (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400035

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