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Crashing a maximum-weight complementary basis

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Abstract

We consider the problem of finding a maximum-weight complementary basis of anm × 2m matrix. The problem arises naturally, for example, when a complementary set of columns is proposed as an initial basis for a “warm start” of Lemke's algorithm, but the set of columns is rank-deficient. We show that the problem is a special case of the problem of finding a maximum-weight common base of two matroids. Furthermore, we show how to efficiently implement an algorithm for the general problem in the present context. Finally, we give computational results demonstrating the practicality of our algorithm in a typical application.

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Authors and Affiliations

  1. Department of Operations Research, Yale University, 06520, New Haven, CT, USA

    Kurt M. Anstreicher & Jon Lee

  2. Department of Economics, University of Western Ontario, N6A 5C2, London, Ont., Canada

    Thomas F. Rutherford

Authors
  1. Kurt M. Anstreicher
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  2. Jon Lee
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  3. Thomas F. Rutherford
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Supported by the Canadian Natural Science and Engineering Research Council.

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Anstreicher, K.M., Lee, J. & Rutherford, T.F. Crashing a maximum-weight complementary basis. Mathematical Programming 54, 281–294 (1992). https://doi.org/10.1007/BF01586055

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  • DOI: https://doi.org/10.1007/BF01586055

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