OPTIMALITY CONDITIONS FOR WEAKLY EFFICIENT SOLUTION OF VECTOR EQUILIBRIUM PROBLEM WITH CONSTRAINTS IN TERMS OF SECOND-ORDER CONTINGENT DERIVATIVES

Authors

  • T. Su Department of Mathematics, Quangnam University, Tamky, Vietnam

Abstract

In this paper, we present second-order necessary and sufficient optimality conditions for weakly efficient solution of a vector equilibrium problem with constraints (in short, VEPC ) in terms of second-order contingent derivative and second-order asymptotic contingent derivative. With this purpose, we impose the objective functions, either all them are twice Fr´echet differentiable at optimal point or the Fr´echet derivatives are calm at optimal point or the profile mappings has the cone-Aubin properties. Besides, we also can invoke constraint qualifications of the Kurcyusz - Robinson - Zowe (KRZ) type. Our paper point out new improvements from the known results of Gutierrez, Jim´enez and Novo (2010) and Khanh and Tung (2015); see [8], [10] in cases of single valued optimization and give some discusses about it.

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Published

2018-02-01

How to Cite

Su, T. (2018). OPTIMALITY CONDITIONS FOR WEAKLY EFFICIENT SOLUTION OF VECTOR EQUILIBRIUM PROBLEM WITH CONSTRAINTS IN TERMS OF SECOND-ORDER CONTINGENT DERIVATIVES. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 7(2), 1-16. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/435

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Section

Research Article