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Zbl 1082.90111
Balaji, R.; Parthasarathy, T.; Sampangi Raman, D.; Vetrivel, V.
On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems. (English)
[J] Math. Oper. Res. 30, No. 2, 462-471 (2005). ISSN 1526-5471; ISSN 0364-765X/e

Summary: 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 $n \times n$ 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.

MSC 2000:: *90C31 Sensitivity, etc.
90C33 Complementarity problems

Keywords: semidefinite linear complementarity problem (SDLCP); Lipschitz continuity; $P$-property; $Q$-property, GUS-property

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