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Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming

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Abstract

In this work we devise efficient algorithms for finding the search directions for interior point methods applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. We summarize earlier results using a modified version of the OB1-R code of Lustig, Marsten, and Shanno, and we present results from a predictor–corrector code PCx modified to use adaptive iteration. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.

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Authors and Affiliations

  1. Department of Mathematics Education, National Tainan Teachers College, Tainan, 700, Taiwan

    Weichung Wang

  2. Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    Dianne P. O'Leary

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  1. Weichung Wang
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  2. Dianne P. O'Leary
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Wang, W., O'Leary, D.P. Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming. Numerical Algorithms 25, 387–406 (2000). https://doi.org/10.1023/A:1016614603137

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