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On the Linear Complementarity Problem

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  • Arza K. Rao

    (Indian Institute of Management, Bangalore)

Abstract

Consider the linear complementarity problem given in the system: where, W, Z and q are vectors of dimension n. M is a matrix of order n \times n and Z T is the transpose of Z. Any (Z, W) satisfying (1), (2), and (3) is a complementary feasible solution to system (I). In the literature, a class of matrices is defined such that if M belongs to this class, then existence of a feasible solution to system (I) implies the existence of a complementary feasible solution to system (I) with W = 0. In this paper, a new class of matrices \scr{M} is developed. It is shown that membership of a matrix M in \scr{M} is equivalent to the property; for any q existence of a feasible solution to system (I) implies the existence of complementary feasible solution to system (I) for that q with W = 0. This new class of matrices is not contained in any one of the known classes, namely, copositive plus, positive definite or semidefinite, P-matrices, P-matrices, Z-class, etc.

Suggested Citation

  • Arza K. Rao, 1975. "On the Linear Complementarity Problem," Management Science, INFORMS, vol. 22(4), pages 427-429, December.
    • Handle: RePEc:inm:ormnsc:v:22:y:1975:i:4:p:427-429
    DOI: 10.1287/mnsc.22.4.427
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    Cited by:

    1. G. S. R. Murthy & K. C. Sivakumar & P. Sushmitha, 2020. "T. Parthasarathy’s contributions to complementarity problems: a survey," Annals of Operations Research, Springer, vol. 287(2), pages 867-894, April.

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