First and second-order optimality conditions using approximations for vector equilibrium problems with constraints

Authors:
Phan Quoc Khanh;Le Thanh Tung
Affiliations:
Department of Mathematics, International University of Hochiminh City, Hochiminh City, Vietnam;Department of Mathematics, College of Sciences, Cantho University, Cantho, Vietnam
Venue:
Journal of Global Optimization
Year:
2013

Citing 7
Cited 0

Optimality conditions via norm scalarization in vector optimization

SIAM Journal on Control and Optimization
Approximations and metric regularity in mathematical programming in Banach space

Mathematics of Operations Research
On the notion of proper efficiency in vector optimization

Journal of Optimization Theory and Applications
Second-Order Conditions for Optimization Problems with Constraints

SIAM Journal on Control and Optimization
Unified representation of proper efficiency by means of dilating cones

Journal of Optimization Theory and Applications
Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces

Journal of Global Optimization
Hölder metric regularity of set-valued maps

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. By using first and second-order approximations as generalized derivatives, we establish both necessary and sufficient optimality conditions. Our first-order conditions are shown to be applicable in many cases, where existing ones cannot be used. The second-order conditions are new.