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Absolute value equation solution via dual complementarity

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Abstract

By utilizing a dual complementarity condition, we propose an iterative method for solving the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving a succession of linear programs. The algorithm was tested on 500 consecutively generated random solvable instances of the AVE with n = 10, 50, 100, 500 and 1,000. The algorithm solved 90.2 % of the test problems to an accuracy of 10−8.

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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. Absolute value equation solution via dual complementarity. Optim Lett 7, 625–630 (2013). https://doi.org/10.1007/s11590-012-0469-5

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  • DOI: https://doi.org/10.1007/s11590-012-0469-5

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