G-α-preinvex functions and non-smooth vector optimization problems

In this paper, we proposed the non-smooth G-?-preinvexity by generalizing ?-invexity and G-preinvexity, and discussed some solution properties about non-smooth vector optimization problems and vector variational-like inequality problems under the condition of non-smooth G-?-preinvexity. Moreover, we also proved that the vector critical points, the weakly efficient points and the solutions of the non-smooth weak vector variational-like inequality problem are equivalent under non-smooth pseudo-G-?-preinvexity assumptions.

A new class of bilevel weak vector variational inequality problems

In this paper, we first introduce a new class of bilevel weak vector variational inequality problems in locally convex Hausdorff topological vector spaces. Then, using the Kakutani-Fan-Glicksberg fixed-point theorem, we establish some existence conditions of the solution for this problem.

Error bounds for generalized mixed weak vector quasiequilibrium problems via regularized gap functions

This paper introduces regularized gap functions for a class of generalized mixed weak vector quasiequilibrium problems. Then, error boundsfor the concerning problems via regularized gap functions are established. Someexamples are provided to illustrate the results.

Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.