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Primal-dual bilinear programming solution of the absolute value equation

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Abstract

We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix. The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program. The proposed algorithm was tested on 500 consecutively generated random instances of the AVE with n = 10, 50, 100, 500 and 1,000. The algorithm solved 88.6% of the test problems to an accuracy of 10−6.

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Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, Madison, WI, 53706, USA

    Olvi L. Mangasarian

  2. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA

    Olvi L. Mangasarian

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  1. Olvi L. Mangasarian
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Correspondence to Olvi L. Mangasarian.

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Mangasarian, O.L. Primal-dual bilinear programming solution of the absolute value equation. Optim Lett 6, 1527–1533 (2012). https://doi.org/10.1007/s11590-011-0347-6

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  • DOI: https://doi.org/10.1007/s11590-011-0347-6

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