A verification method for solutions of linear programming problems

Abstract

This paper is concerned with the verification of a solution of a linear programming problem obtained by an interior-point method. The presented method relies on a reformulation of the linear programming problem as an equivalent system of nonlinear equations and uses mean value interval extension of functions and a computational fixed point theorem. The designed algorithm proves or disproves the existence of a solution on a computer and, if it exists, encloses this solution in narrow bounds. © Springer-Verlag Berlin Heidelberg 2006.