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A note on an open problem in linear complementarity

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Abstract

LetK be the class ofn × n matricesM such that for everyn-vectorq for which the linear complementarity problem (q, M) is feasible, then the problem (q, M) has a solution. Recently, a characterization ofK has been obtained by Mangasarian [5] in his study of solving linear complementarity problems as linear programs. This note proves a result which improves on such a characterization.

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References

  1. R.W. Cottle and J.S. Pang, “On solving linear complementarity problems as linear programs”, Tech. Rept. SOL 76-5, Systems Optimization Laboratory, Stanford University, Stanford (March 1976).

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  2. R.W. Cottle and J.S. Pang, “A least-element theory of solving linear complementarity problems as linear programs”, MRC Tech. Rept. #1702, Mathematics Research Center, University of Wisconsin-Madison (December 1976).

  3. O.L. Mangasarian, “Linear complementarity problems solvable by a single linear program”,Mathematical Programming 10 (1976) 263–270.

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  4. O.L. Mangasarian, “Solution of linear complementarity problems by linear programming”, in: G.W. Watson, ed.,Numerical analysis, Dundee 1975, Lecture Notes in Mathematics, No. 506 (Springer, Berlin, 1976) pp. 166–175.

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  5. O.L. Mangasarian, “Characterization of linear complementarity problems as linear programs”, Tech. Rept. 271, Computer Sciences Department, University of Wisconsin-Madison (May 1976).

  6. J.S. Pang, “Least element complementarity theory”, Ph.D. dissertation, Department of Operations Research, Stanford University (September 1976).

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Authors and Affiliations

  1. University of Wisconsin-Madison, Madison, WI, USA

    Jong-Shi Pang

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  1. Jong-Shi Pang
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Additional information

Research sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and the National Science Foundation under Grant No. MCS75-17385.

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Pang, JS. A note on an open problem in linear complementarity. Mathematical Programming 13, 360–363 (1977). https://doi.org/10.1007/BF01584349

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  • DOI: https://doi.org/10.1007/BF01584349

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