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The basic theorem of complementarity revisited

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Abstract

The basic theorm of (linear) complementarity was stated in a 1971 paper [6] by B.C. Eaves who credited C.E. Lemke for giving a constructive proof based on his almost complementary pivot algorithm. This theorem asserts that associated with an arbitrary linear complementarity problem, a certain augmented problem always possesses a solution. Many well-known existence results pertaining to the linear complementarity problem are consequences of this fundamental theorem.

In this paper, we explore some further implications of the basic theorem of complementarity and derive new existence results for the linear complementarity problem. Based on these results, conditions for the existence of a solution to a linear complementarity problem with a fully-semimonotone matrix are examined. The class of the linear complementarity problems with aG-matrix is also investigated.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Maryland Baltimore County, 21228, Baltimore, MD, USA

    M. Seetharama Gowda

  2. Department of Mathematical Sciences, The Johns Hopkins University, 21218, Baltimore, MD, USA

    Jong-Shi Pang

Authors
  1. M. Seetharama Gowda
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  2. Jong-Shi Pang
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The work of this author was based on research supported by the National Science Foundation under grant ECS-8717968.

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Gowda, M.S., Pang, JS. The basic theorem of complementarity revisited. Mathematical Programming 58, 161–177 (1993). https://doi.org/10.1007/BF01581265

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  • DOI: https://doi.org/10.1007/BF01581265

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