Optimality conditions in a class of generalized convex optimization problems with the multiple interval-valued objective function

Abstract

In this paper, a new class of generalized convex optimization problems with a multiple interval-valued objective function is considered. The concepts of B-preinvexity, B-invexity, and the generalized of B-invexity are extended to interval-valued functions. Additionally, several properties of interval-valued B-preinvex and B-invex functions are investigated. The Karush–Kuhn–Tucker necessary optimality conditions for a (weak LU-Pareto) LU-Pareto solution are established for a differentiable vector optimization problem with a multiple interval-valued objective function. Furthermore, the sufficient optimality conditions for both LU and UC order relations are derived for such interval-valued vector optimization problems under appropriate (generalized) B-invexity hypotheses. Suitable examples are provided to illustrate the aforementioned results.

Keywords

• Interval-valued functions
• Generalized convexity
• B-invex function
• Optimality conditions