On the Linear Complementarity Problem

Arza K. Rao
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Arza K. Rao: Indian Institute of Management, Bangalore

Management Science, 1975, vol. 22, issue 4, 427-429

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.

Date: 1975
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