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Cuiting Fan, Guolin Yu, Shengxin Hua, Optimality and scalarization of approximate solutions for vector equilibrium problems via Michel-Penot subdifferential

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DOI: 10.23952/asvao.6.2024.2.07
Volume 6, Issue 2, 1 August 2024, Pages 233-244

 

Abstract. This paper is devoted to the investigation of the optimality and scalarization for approximate solutions to a Constrained Vector Equilibrium Problem (CVEP). The optimality conditions are given in terms of Michel-Penot subdifferentials, and the scalarization theorems are proposed via a strongly monotone cone convex function. We firstly establish a necessary condition for an approximate quasi weakly efficient solution to problem (CVEP). Then, a sufficient condition for approximate quasi Benson proper efficient solutions to problem (CVEP) is examined under the newly introduced generalized convexity assumptions. Finally, by using the properties of Bishop-Phelps cone, we present the scalarization theorems for approximate quasi weakly (Benson proper) efficient solutions.

 
How to Cite this Article:
C. Fan, G. Yu, S. Hua, Optimality and scalarization of approximate solutions for vector equilibrium problems via Michel-Penot subdifferential, Appl. Set-Valued Anal. Optim. 6 (2024), 233-244.