Dual–primal algorithm for linear optimization

Abstract

The purpose of this paper is to present a new approach for solving linear programming, which has some interesting theoretical properties. In each step of the iteration, we trace a direction completely different from primal simplex method, dual simplex method, primal–dual method and interior point method. The new method is impervious to primal degeneracy and can reach a pair of exact primal and dual optimal solutions without purifying process. Numerical results are presented that support our theoretical results and confirm the viability of the approach.