Crashing a maximum-weight complementary basis |
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Authors: | Kurt M Anstreicher Jon Lee Thomas F Rutherford |
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Institution: | (1) Department of Operations Research, Yale University, 06520 New Haven, CT, USA;(2) Department of Economics, University of Western Ontario, N6A 5C2 London, Ont., Canada |
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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.Supported by the Canadian Natural Science and Engineering Research Council. |
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Keywords: | Linear complementarity problem Lemke's algorithm matroid intersection |
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