On nondifferentiable semi-infinite multiobjective programming with interval-valued functions

Abstract

In the paper, we investigate a class of nondifferentiable semi-infinite multiobjective programming problems such that all functions constituting them are interval-valued. We derive both Fritz John necessary optimality conditions and, under a constraint qualification, Karush-Kuhn-Tucker necessary optimality conditions for (weak) $ LU $-Pareto solutions in the considered nondifferentiable semi-infinite vector interval-valued optimization problem. Under appropriate invexity hypotheses, we also prove sufficient optimality conditions for this semi-infinite interval-valued vector optimization problem. Further, we also use the $ l_{1} $ exact function method for solving the aforesaid nondifferentiable interval-valued multicriteria optimization problem. Then, we analyze the property of exactness of the penalization for the absolute value exact penalty function method under assumption that the functions involved in the considered semi-infinite multiobjective programming problem are locally Lipschitz interval-valued invex functions. The conditions guaranteeing the equivalence of the sets of (weak) $ LU $-Pareto solutions in the original semi-infinite interval-valued multiobjective programming problem and its associated vector penalized optimization problem with the multiple interval-valued $ l_{1} $ exact penalty function are given.