Checking Existence of Tolerance Solutions of Interval Linear Equations via Mixed Integer Programming

Abstract

An approach to deal with interval linear equations is to reduce the problem into solving several linear (or nonlinear) equations (or inequalities). To obtain characterations of the equations the paper gives a necessary condition of tolerance solutions of interval linear equations by means of nonlinear inequalities. Based on the necessary condition, a sufficience condition for nonexistence of tolerance solutions of the equations is given by use of the well-known Farkas theorem.