Vector optimization problem and generalized convexity

Abstract

Non smooth functions, Limiting subdifferential, Pseudoinvex functions, Vector variational-like inequalities, Vector optimization problems,

On local quasi efficient solutions for nonsmooth vector optimization problems

“…For differentiable and convex multiobjective functions, Giannessi [13] used vector variational inequalities of Minty type [17] to derive necessary and sufficient conditions for efficient solutions. Generalizations of these optimality conditions were given for different types of generalized convexity [1,10,11,21,23] and generalized invexity [3,16,18,24]. In [19], relationships between quasi efficient points, solutions to Stampacchia vector variational inequalities and vector critical points were identified under approximate convexity assumptions.…”

On local quasi efficient solutions for nonsmooth vector optimization

“…For differentiable and convex multiobjective functions, Giannessi [5] used vector variational inequalities of Minty type [6] to derive necessary and sufficient conditions for efficient solutions. Generalizations of these optimality conditions were given for different types of generalized convexity [7,8,9,10,11] and generalized invexity [12,13,14,15]. In [16], relationships between quasi efficient points, solutions to Stampacchia vector variational inequalities and vector critical points were identified under approximate convexity assumptions.…”