Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems

Jia-Wei Chen (), Zhongping Wan () and Yeol Cho ()

Mathematical Methods of Operations Research, 2013, vol. 77, issue 1, 33-64

Abstract: This paper is devoted to the Levitin–Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with respect to a parameter (PSSVQEP) and its dual problem are established. Some sufficient and necessary conditions for the Levitin–Polyak well-posedness by perturbations are derived by the method of continuous selection. We also explore the relationships among these Levitin–Polyak well-posedness by perturbations, the existence and uniqueness of solution to (SSVQEP). By virtue of the nonlinear scalarization technique, a parametric gap function g for (PSSVQEP) is introduced, which is distinct from that of Peng (J Glob Optim 52:779–795, 2012 ). The continuity of the parametric gap function g is proved. Finally, the relations between these Levitin–Polyak well-posedness by perturbations of (SSVQEP) and that of a corresponding minimization problem with functional constraints are also established under quite mild assumptions. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: System of set-valued vector quasi-equilibrium problem; Existence theorem; Levitin–Polyak well-posedness by perturbations; Parametric gap function; Nonlinear scalarization function; 49J40; 49K40; 90C33 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00186-012-0414-5

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