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A quadratically convergent predictor—corrector method for solving linear programs from infeasible starting points

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Abstract

A predictor—corrector method for solving linear programs from infeasible starting points is analyzed. The method is quadratically convergent and can be combined with Ye's finite termination scheme under very general assumptions. If the starting points are large enough then the algorithm hasO(nL) iteration complexity. If the ratio between feasibility and optimality at the starting points is small enough then the algorithm has O(\(\sqrt {n L} \)) iteration complexity. For feasible starting points the algorithm reduces to the Mizuno—Todd—Ye predictor—corrector method.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, 52240, Iowa City, IA, USA

    Florian A. Potra

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  1. Florian A. Potra
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This work was supported by an interdisciplinary research grant from the Institute for Advanced Studies of the University of Iowa.

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Potra, F.A. A quadratically convergent predictor—corrector method for solving linear programs from infeasible starting points. Mathematical Programming 67, 383–406 (1994). https://doi.org/10.1007/BF01582228

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  • DOI: https://doi.org/10.1007/BF01582228

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