TY - JOUR

T1 - Sufficient matrices and the linear complementarity problem

AU - Cottle, R. W.

AU - Pang, J. S.

AU - Venkateswaran, V.

N1 - Funding Information:
‘Research partially supported by the National Science Foundation Grant DMS-8420823, U.S. Department of Energy Grant GEFGO387ER25028, and Office of Naval Research Contract
Funding Information:
2Research partially supported by the National Science Foundation Grant ECS-8644098.

PY - 1989

Y1 - 1989

N2 - We pose and answer two questions about solutions of the linear complementarity problem (LCP). The first question is concerned with the conditions on a matrix M which guarantee that for every vector q, the solutions of the LCP (q, M) are identical to the Karush-Kuhn-Tucker points of the natural quadratic program associated with (q, M). In answering this question we introduce the class of "row sufficient" matrices. The transpose of such a matrix is what we call "column sufficient". The latter matrices turn out to furnish the answer to our second question, which asks for the conditions on M under which the solution set of (q, M) is convex for every q. In addition to these two main results, we discuss the connections of these twonew matrix classes with other well-known matrix classes in linear complementarity theory.

AB - We pose and answer two questions about solutions of the linear complementarity problem (LCP). The first question is concerned with the conditions on a matrix M which guarantee that for every vector q, the solutions of the LCP (q, M) are identical to the Karush-Kuhn-Tucker points of the natural quadratic program associated with (q, M). In answering this question we introduce the class of "row sufficient" matrices. The transpose of such a matrix is what we call "column sufficient". The latter matrices turn out to furnish the answer to our second question, which asks for the conditions on M under which the solution set of (q, M) is convex for every q. In addition to these two main results, we discuss the connections of these twonew matrix classes with other well-known matrix classes in linear complementarity theory.

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U2 - 10.1016/0024-3795(89)90463-1

DO - 10.1016/0024-3795(89)90463-1

M3 - Article

AN - SCOPUS:0001456864

VL - 114-115

SP - 231

EP - 249

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - C

ER -