On interval-valued vector variational-like inequalities and vector optimization problems with generalized approximate invexity via convexificators

Abstract

In this paper, we establish the relationships between a class of interval-valued vector optimization problems and interval-valued vector variational-like inequality problems of both Stampacchia and Minty kinds in terms of convexificators. We also provide necessary and sufficient optimality requirements for locally strong quasi and approximately efficient solutions by using the concept of approximate LU-(η, e)-invexity. Numerical example is also presented to validate the main result. Our newly proved results generalize some well-known results in the literature.

On Approximate Variational Inequalities and Bilevel Programming Problems

“…Variational inequalities have several applications in the fields of economics, game theory, and traffic analysis (see [38,39] and the references cited therein). Variational inequality problems have been studied by several scholars as tools for solving optimization problems, for more exposition (see, [40][41][42][43][44][45][46][47][48][49][50][51][52] in the Euclidean space setting and [53][54][55] on Hadamard manifolds). Komlósi [56] derived the equivalence among the solutions of Minty and Stampacchia variational inequality and the optimal solution of the minimization problem.…”