Existence of solution of constrained interval optimization problems with regularity concept

Abstract

Objective of this article is to study the conditions for the existence of efficient solution of interval optimization problem with inequality constraints. Here the active constraints are considered in inclusion form. The regularity condition for the existence of the Karush -Kuhn-Tucker point is derived. This condition depends on the interval-valued gradient function of active constraints. These are new concepts in the literature of interval optimization. gH -differentiability is used for the theoretical developments. gH -pseudo convexity for interval valued constrained optimization problems is introduced to study the sufficient conditions. Theoretical developments are verified through numerical examples.

Fréchet subdifferential calculus for interval-valued functions and its applications in nonsmooth interval optimization

“…Definition 2.16. (gH-gradient [43]). The gH-gradient of a proper extended IVF F at a point x 0 ∈ X is defined by the vector…”