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Date Published: 27/02/2023
Online Published: 28/02/2023
Abstract Views: 57
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Issue
Vol. 1 No. 4 (2022)
Section
Articles
How to Cite
Do, V. L., & Tran, T. M. (2023). OPTIMALITY CONDITIONS FOR EFFICIENCY OF CONSTRAINED VECTOR EQUILIBRIUM PROBLEMS. Thang Long Journal of Science: Mathematics and Mathematical Sciences, 1(4), 67-85. https://science.thanglong.edu.vn/index.php/volc/article/view/49

OPTIMALITY CONDITIONS FOR EFFICIENCY OF CONSTRAINED VECTOR EQUILIBRIUM PROBLEMS

Van Luu Do1,, Thi Mai Tran2
1 Thang Long Institute of Mathematics and Applied Sciences
2 University of Economics and Business Administration

Main Article Content

Abstract

Fritz John necessary conditions for local Henig and global efficient solutions of vector equilibrium problems involving equality, inequality and set constraints with nonsmooth functions are established via convexificators. Under suitable constraint qualications, Kuhn-Tucker necessary conditions for local Henig and gobally efficient solutions are derived. Note that Henig and global efficient solutions of (VEP) are studied with respect to a closed convex cone. Sufficient condition for Henig and globally efficient solutions are derived under some assumptions on asymptotic semiinvexityinfne of the problem. Some illustrative examples are also given.

Article Details

Keywords

Local Henig efficient solution, local global solution, vector equilibrium problems, Fritz John and Kuhn-Tucker necessary conditions, convexificators

References

[1] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983.
[2] T. D. Chuong, L-invex-infine functions and applications, Nonlinear Anal.,75 (2012), 5044-5052.
[3] P. Daniele, Lagrange multipliers and infinite-dimensional equilibrium problems, J. Glob. Optim., 40 (2008), 65-70.
[4] F. Giannessi, G. Mastroeni and L. Pellegrini, On the theory of vector optimization and variational inequalities, image space analysis and separation, in: Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, F. Giannessi (ed.), Kluwer, Dordrecht, 2000, 153-215.
[5] X. H. Gong, Scalarization and optimality conditions for vector equilibrium problems, Nonlinear Anal., 73 (2010), 3598-3612.
[6] I. V. Girsanov, Lectures on Mathematical Theory of Extremum Problems, Berlin-Heidenberg, Springer-Verlag, 1972.
[7] V. Jeyakumar and D. T. Luc, Nonsmooth calculus, minimality, and mono-tonicity of convexificators, J. Optim. Theory Appl., 101 (1999), 599-621.
[8] X. J. Long, Y. Q. Huang and Z. Y. Peng, Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints,Optim. Lett., 5 (2011), 717-728.
[9] J. Morgan and M. Romaniello, Scalarization and Kuhn-Tucker-like conditions for weak vector generalized quasivariational inequalities, J. Optim.Theory Appl., 130 (2006), 309-316.
[10] D. V. Luu, D. D. Hang, On optimality conditions for vector variational inequalities, J. Math. Anal. Appl., 412 (2014), 792-804.
[11] D. V. Luu, D. D. Hang, Efficient solutions and optimality conditions for vector equilibrium problems, Math. Meth. Oper. Res., 79 (2014), 163-177.
[12] D. V. Luu, Necessary and sufficient conditions for efficiency via convexificators, J. Optim. Theory Appl., 160 (2014), 510-526.
[13] D. V. Luu, Necessary conditions for efficiency in terms of the Michel-Penot subdifferentials, Optimization, 61 (2012), 1099-1117.
[14] D. V. Luu, Optimality condition for local e cient solutions of vector equilibriuam problems via convexificators and applications, J. Optim. Theory Appl., 171 (2016), 643-665.