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On the Lipschitz Continuity of the Solution Map in Semidefinite Linear Complementarity Problems

Department of Mathematics, Indian Institute of Technology-Madras, Chennai-600036, India
Department of Mathematics and Statistics, University of Hyderabad, Hyderabad-500046, India
Indian Statistical Institute, Nelson Manickam Road, Nungambakkam, Chennai-600029, India
Department of Mathematics, Indian Institute of Technology-Madras, Chennai-600036, India
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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 x 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-property.

Key Words: semidefinite linear complementarity problem (SDLCP); Lipschitz continuity; P-property; Q-property; GUS-property
History: Received: November 12, 2003; revision received: June 24, 2004;