Jacek Gondzio

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A modiication of the (infeasible) primal{dual interior point method is developed. The method uses multiple corrections to improve the centrality of the current iterate. The maximum number of corrections the algorithm is encouraged to make depends on the ratio of the eeorts to solve and to factorize the KKT systems. For any LP problem, this ratio is(More)
Every Newton step in an interior-point method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail(More)
Issues of implementation of an object-oriented library for parallel interior-point methods are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modelled. The efficiency of(More)
This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of recentering in the implementation of interior point methods. Second-order correctors, such as(More)
Several issues concerning an analysis of large and sparse linear programming problems prior to solving them with an interior point based optimizer are addressed in this paper. Three types of presolve procedures are distinguished. Routines from the rst class repeatedly analyze an LP problem formulation: eliminate empty or singleton rows and columns, look for(More)
One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced starting point which(More)
The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a(More)
Re-optimization techniques for an interior point method applied to solve a sequence of linear programming problems are discussed. Conditions are given for problem perturbations that can be absorbed in merely one Newton step. The analysis is performed for both short-step and long-step feasible path-following method. A practical procedure is then derived for(More)
Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their(More)