A Modified Infeasible-Interior-Point Algorithm for Linear Optimization Problems

Abstract

In this paper, we present an improved version of the infeasible-interiorpoint method for linear optimization introduced by Roos (SIAM J Optim 16 (4): 2006). Each main step of Roos's algorithm is composed of one feasibility step and several centering steps. By using a new search direction, we prove that it is enough to take only one step in order to obtain a polynomial-time method. The iteration bound coincides with the currently best iteration bound for linear optimization problems.

An Adaptive Primal-Dual Full-Newton Step Infeasible Interior-Point Algorithm for Linear Optimization

“…In this section we solve some LO problems from NETLIB by the original Roos's infeasible algorithm [8], and by short updating algorithm [6], as well as by the adaptive updating algorithm in Figure 1. For all these cases, the initialization parameter ζ is calculated as described in Section 2 correspond to some obtained optimal solutions of the problems by the feasible interior-point algorithm in [8].…”

“…Similar to [6], we replace the right hand side of the nonlinear equation xs = µe with µv in which v is the variance vector corresponding to x and s. Define…”

“…Subsequently, some authors have tried to improve the Roos's infeasible algorithm, see for example [4,5]. Some improvements have done in order to reduce or remove the centering steps [1,6,9,14].…”

“…Recently, Mansouri et al [6] proposed an IIPM for solving LO problems with a reformulation of the central path. Their algorithm need not to perform any centering step to reach the closeness of the iterates to their µ-centers.…”

“…In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al [6]. The algorithm takes only one full-Newton step in a major iteration.…”