This note derives bounds on the length of the primal-dual affine scaling directions associated with a linearly constrained convex program satisfying the following conditions: 1) the problem has a solution satisfying strict complementarity, 2) the Hessian of the objective function satisfies a certain invariance property. We illustrate the usefulness of these bounds by establishing the superlinea...

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primal-dual infeasibleinterior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an a...

The paper is a simplified exposition of an early combined phase I-phase II method for linear programming. The method works from an infeasible start. Besides, there is no need for regularity conditions if the method is applied to a primal-dual formulation.

The Mizuno-Todd-Ye predictor-corrector algorithm for linear programming is extended for solving monotone linear complementarity problems from infeasible starting points. The proposed algorithm requires two matrix factorizations and at most three backsolves per iteration. Its computational complexity depends on the quality of the starting point. If the starting points are large enough, then the ...

A practical warm-start procedure is described for the infeasible primal-dual interior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this eld, the approach presented in this paper does not make the unrealistic assumption that the new cuts are shallow. Moreover, it treats systematically the case when a ...

Interior-point methods for nonlinear programming have been demonstrated to be quite efficient, especially for large scale problems, and, as such, they are ideal candidates for solving the nonlinear subproblems that arise in the solution of mixed-integer nonlinear programming problems via outer approximation. However, traditionally, infeasible primal-dual interior-point methods have had two main...

This paper describes interior point methods for nonlinear programming endowed with infeasibility detection capabilities. The methods are composed of two phases, a main phase whose goal is to seek optimality, and a feasibility phase that aims exclusively at improving feasibility. A common characteristic of the algorithms is the use of a step-decomposition interior-point method in which the step ...

Despite the many advantages of interior-point algorithms over active-set methods for linear optimization, one of the remaining practical challenges is their current limitation to efficiently solve series of related problems by an effective warmstarting strategy. In its remedy, in this paper we present a new infeasible-interior-point approach to quickly re-optimize an initial problem instance af...

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. New regularization techniques for Newton systems applicable to both symmetric positive de nite and symmetric inde nite systems are described. They transform the latter to quaside nite systems known to be strongly ...

In this paper, we first present a brief review about the feasible interior-point algorithm for P∗(κ)-horizontal linear complementarity problems (HLCPs) based on new directions. Then we present a new infeasible interior-point algorithm for these problems. The algorithm uses two types of full-Newton steps which are called feasibility steps and centering steps. The algorithm starts from strictly f...