Motivated by the so-called P2-property in the semidefinite linear complementarity problems, in this article, we introduce the concept of P2′-property for a linear transformation on the space of real n × n symmetric matrices. While these two properties turn out to be different, we show that they are equivalent for the Lyapunov transformation LA, double-sided multiplicative transformation MA and a particular class of Stein transformations. We also show that P2′ implies the SSM and Q-properties. © 2009.

V. Vetrivel

Department of Mathematics

LINEAR TRANSFORMATION

LYAPUNOV TRANSFORMATION

P2-PROPERTY

Q-PROPERTIES

SEMIDEFINITE LINEAR COMPLEMENTARITY PROBLEM

SEMIDEFINITE LINEAR COMPLEMENTARITY PROBLEM (SDLCP)

SYMMETRIC MATRICES

Linear algebra

Mathematical techniques

Equivalence classes

Fulltext

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IIT Madras

Linear Algebra and Its Applications

In this paper, we investigate the Lipschitz continuity of the solution map in semidefinite linear complementarity problems. For a monotone linear transformation defined on the space of real symmetric n × n matrices, we show that the Lipschitz continuity of the solution map implies the globally uniquely solvable (GUS)-property. For Lyapunov transformations with the Q-property, we prove that the Lipschitz continuity of the solution map is equivalent to the strong monotonicity property. For the double-sided multiplicative transformations, we show that the Lipschitz continuity of the solution map implies the GUS-propeity. © 2005 INFORMS.

Mathematics of Operations Research

On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems

Mathematical Programming

Z-transformations on proper and symmetric cones

The Linear Complementarity Problem

The Electronic Journal of Linear Algebra

The Q-property of a multiplicative transformation in semidefinite linear complementarity problems

Linear Algebra and its Applications

On some interconnections between strict monotonicity, globally uniquely solvable, and P properties in semidefinite linear complementarity problems

On the P2′ and P2-properties in the semidefinite linear complementarity problem

Journal	Linear Algebra and Its Applications
ISSN	00243795
Open Access	Yes