Warm Start and ε-Subgradients in a Cutting Plane Scheme

Authors:
J. Gondizo;J.-P Vial
Affiliations:
Logilab, HEC, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Genève 4, Switzerland;Logilab, HEC, Section of Management Studies, University of Geneva, 102 Bd Carl Vogt, CH-1211 Genève 4, Switzerland
Venue:
Computational Optimization and Applications
Year:
1999

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Abstract

This paper addresses the issues involved with aninterior point-based decomposition applied to the solution oflinear programs with a block-angular structure. Unlike classicaldecomposition schemes that use the simplex method to solvesubproblems, the approach presented in this paper employs aprimal-dual infeasible interior point method. Theabove-mentioned algorithm offers a perfect measure of thedistance to optimality, which is exploited to terminate thealgorithm earlier (with a rather loose optimality tolerance) andto generate ε-subgradients. In the decompositionscheme, subproblems are sequentially solved for varyingobjective functions. It is essential to be able to exploit theoptimal solution of the previous problem when solving asubsequent one (with a modified objective). A warm start routineis described that deals with this problem. The proposed approach has been implemented within the context of two optimization codes freely available for research use: the Analytic Center Cutting Plane Method (ACCPM)—interior point based decomposition algorithmand the Higher Order Primal-Dual Method (HOPDM)—general purpose interior point LP solver. Computational results are given to illustrate the potential advantages of the approach applied to the solution of very large structured linear programs.