5 research outputs found
Penalization for variational inequalities
AbstractThis work illustrates a penalization mechanism, using the distance function as a tool, for providing necessary and sufficient conditions for the solutions of the nonsmooth variational inequality problems
Some relations between Minty variational-like inequality problems and vectorial optimization problems in Banach spaces
This paper is devoted to the study of relationships between solutions of Stampacchia
and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector
optimization problems and vector critical points in Banach spaces under pseudo-invexity
and pseudo-monotonicity hypotheses. We have extended the results given by Gang and
Liu (2008) [22] to Banach spaces and the relationships obtained for weak efficient points
in Santos et al. (2008) [21] are completed and enabled to relate vector critical points,
weak efficient points, solutions of the Minty and Stampacchia weak vector variationallike inequalities problems and solutions of perturbed vector variational-like inequalities
problems
Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps
We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence result of generalized weakly efficient solutions for vector optimization problem involving a subdifferentiable and preinvex set-valued mapping is established by exploiting the existence of a solution for the weak formulation of the generalized Stampacchia vector variational-like inequality via a Fan-KKM lemma