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On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems. (English) Zbl 1082.90111
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×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:
90C31Sensitivity, stability, parametric optimization
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)