Checking weak optimality of the solution to interval linear program in the general form

Abstract

One of the basic and difficult tasks in interval linear programming (IvLP) problems is to check whether a given point is weak optimal. In this paper, we investigate IvLP problem in the general form, in which the constraints contain mixed interval linear equations and inequalities with both non-negative and free variables. Necessary and sufficient conditions for checking weak optimality of a given vector are established, based on the KKT conditions of linear programming and the newly established weak solvability characterizations of mixed interval linear systems by Hladik. The result solves one of the open problems proposed by Hladik (Linear Programming New Frontiers. Nova Science Publishers, Inc 2012).