Checking solvability of systems of interval linear equations and inequalities via mixed integer programming

This paper deals with the problems of checking strong solvability and feasibility of linear interval equations, checking weak solvability of linear interval equations and inequalities, and finding control solutions of linear interval equations. These problems are known to be NP -hard. We use some recently developed characterizations in combination with classical arguments to show that these problems can be equivalently stated as optimization tasks and provide the corresponding linear mixed 0–1 programming formulations.