Linear complementarity problem: Difference between revisions

Revision as of 14:32, 12 September 2015

Revision as of 15:04, 12 September 2015

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A sufficient condition for existence and uniqueness of a solution to this problem is that '''M''' be [[Symmetric matrix|symmetric]] [[Positive-definite matrix|positive-definite]].

If '''M''' is such that the problem'''LCP(M,q)''' have a solution for every '''q''', then '''M''' is a [[Q-matrix]]. If '''M''' is such that the problem'''LCP(M,q)''' have an unique solution for every '''q''',

then '''M''' is a [[P-matrix]]. Both of these characterizations are sufficient and necessary.<ref>{{cite journal|last1=Murty|first1=Katta G.|title=On the number of solutions to the complementarity problem and spanning properties of complementary cones|journal=Linear Algebra and its Applications|date=January 1972|volume=5|issue=1|pages=65–108|doi=10.1016/0024-3795(72)90019-5}}</ref>