In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty Vector variational-like inequality,  the Stampacchia Vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the Vector variational-like inequalities and Vector optimization problems are established.

In this paper, we establish weak and strong duality theorems for a pair of multi-objective symmetric dual problems. This removes several omissions in the paper "Symmetric and self-duality in Vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

In this paper, the class of nonconvex Vector-valued optimization problems with inequality constraints is considered. We introduce two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker type of necessary conditions for a (weakly) efficient solution to the considered problem. All results are given in terms of Dini directional derivative and Clarke subdifferential.

In this article, we examine a nonsmooth Vector optimization problem with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type Vector variational inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth Vector optimization problems using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings.

This paper studies some existence results for generalized e-Vector equilibrium problems and generalized e-Vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

The purpose of this paper is to study the solvability for a class of generalized strong Vector equilibrium-like problems in reflexive Banach spaces. Firstly, utilizing Brouwer’s fixed point theorem, we prove the solvability for this class of generalized strong Vector equilibrium-like problems without monotonicity assumption. Secondly, we introduce the new concept of pseudomonotonicity for Vector set-valued mapping and prove the solvability for this class of generalized strong Vector equilibrium-like problems for pseudomonotone Vector set-valued mapping by using Fan’s lemma and Nadler’s theorem. Our results extend and improve the corresponding results in this direction.