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    Publication
    On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems
    (01-05-2005) ;
    Parthasarathy, T.
    ;
    Raman, D. Sampangi
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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 × 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.
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    Publication
    On the Lipschitz continuity of the solution map in linear complementarity problems over second-order cone
    (01-12-2016) ;
    Palpandi, K.
    Let K⊆IRn denote the second-order cone. Given an n×n real matrix M and a vector q∈IRn, the second-order cone linear complementarity problem SOLCP(M,q) is to find a vector x∈IRn such thatx∈K,y:=Mx+q∈KandyTx=0. We say that M∈Q if SOLCP(M,q) has a solution for all q∈IRn. An n×n real matrix A is said to be a Z-matrix with respect to K iff:x∈K,y∈KandxTy=0  ⟹xTMy≤0. Let ΦM(q) denote the set of all solutions to SOLCP(M,q). The following results are shown in this paper: • If M∈Z∩Q, then ΦM is Lipschitz continuous if and only if M is positive definite on the boundary of K.• If M is symmetric, then ΦM is Lipschitz continuous if and only if M is positive definite.