Article Sidebar

PDF
Date Published: 25/12/2019
Online Published: 25/12/2019
Abstract Views: 48
Views PDF: 37
DOI: https://doi.org/10.52714/dthu.41.12.2019.752
Issue
No. 41 (2019): Part B - Natural Sciences
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Tran, V. S., Nguyen, T. P., Tran, N. Q., & Nguyen, T. B. L. (2019). Necessary efficiency conditions for the local superefficient solutions of vector equilibrium problems with general inequality constraints and applications. Dong Thap University Journal of Science, 41, 74-80. https://doi.org/10.52714/dthu.41.12.2019.752

Necessary efficiency conditions for the local superefficient solutions of vector equilibrium problems with general inequality constraints and applications

Van Su Tran1, Thanh Phong Nguyen1, Ngoc Quoc Tran1, Thi Bich Lai Nguyen1
1 Quang Nam University

Main Article Content

Abstract

In this article, we use the concept of Studniarski’s derivatives in Banach spaces with a class of non-smooth functions to establish necessary efficiency conditions for the local superefficient solution of vector equilibrium problem with a set constraint and a general inequality constraint. The obtained results are directly applied to the vector variational inequality problem and the vector optimization problem with their common set and general inequality constraints.

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

Necessary efficiency conditions, Vector equilibrium problems, Vector optimization problems, Vector variational inequality problems, Local superefficient solutions, Studniarski’s derivatives

References

[1]. Q. H. Ansari (2000), “Vector Equilibrium Problems and Vector Variational Inequalities, in Vector Variational Inequalities and Vector EquilibriaMathematical Theories”, Edited by Prof. F. Giannessi, Kluwer Academic Publishers, Dordrecht-Boston-London, pp. 1-16.
[2]. M. Bianchi, N. Hadjisavvas, S. Schaible (1997), “Vector equilibrium problems with generalized monotone bifunctions”, J. Optim. Theory Appl., (92), pp. 527-542.
[3]. E. Blum, W. Oettli (1994), “From optimization and variational inequalities to equilibrium problems”, Math. Stud., (63), pp. 127-149.
[4]. G. Giorgi, A. Guerraggio (1992), On the notion of tangent cone in mathematical programming, Optimization, (25), pp. 11-23.
[5]. X. H. Gong (2010), “Scalarization and optimality conditions for vector equilibrium problems”, Nonlinear Analysis, (73), pp. 3598-3612.
[6]. A. D. Ioffe (1984), “Calculus of dini subdifferentials of functions and contingent coderivatives of set-valued maps”, Nonlinear Analysis: Theory , Methods & Applications, 3 (5), pp. 517-539.
[7]. P. Q. Khanh, N. M. Tung (2015), “Optimization conditions and duality for nonsmooth vector equilibrium problems with constraints”, Optimization, (64), pp. 1547-1575.
[8]. X. J. Long, Y. Q. Huang, Z. Y. Peng (2011), “Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints”, Optim. Lett., (5), pp. 717-728.
[9]. D. V. Luu (2008), “Higher-order necessary and sufficient conditions for strict local Pareto minima in terms of Studniarski's derivatives”, Optimization, (57), pp. 593-605.
[10]. R. T. Rockafellar (1970), Convex Analysis, Princeton Univ. Press, Princeton.
[11]. M. Studniarski (1986), Necessary and sufficient conditions for isolated local minima of nonsmooth functions, SIAM J. Optim., (24), pp. 1044-1049.