A Genuine Quadratically Convergent Polynomial Interior Point Algorithm for Linear Programming

Abstract

It is well-known that the predictor-corrector method for linear programming has O(√nL) iteration complexity and local quadratic convergence. However, at each iteration the predictor-corrector method requires solving two linear systems, thus making it a two-step quadratically convergent method. In this paper, we propose a variant of the O(√nL)-iteration interior point algorthm for linear programming. Unlike the predictor-corrector method, the variant has a genuine quadratic convergence rate since each iteration involves solving only one linear system. Other features of the algorithm include the gradual phasing out of the centering direction when approaching optimality. Our work is based on the recent results of Gonzaga and Tapia [1,2] about the iterate convergence of the predictor-corrector method, and it does not require any nondegeneracy assumption.