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• W2051601976 abstract "This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R 0-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically." @default.
• W2051601976 created "2016-06-24" @default.
• W2051601976 creator A5052052637 @default.
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• W2051601976 date "2006-01-01" @default.
• W2051601976 modified "2023-10-18" @default.
• W2051601976 title "Some geometrical aspects of semidefinite linear complementarity problems" @default.
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• W2051601976 doi "https://doi.org/10.1080/03081080512331318463" @default.
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