Now showing 1 - 3 of 3
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    On the Lipschitz continuity of the solution map in semidefinite linear complementarity problems
    (01-05-2005) ;
    Parthasarathy, T.
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    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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    A uniqueness result for linear complementarity problems over the Jordan spin algebra
    (15-08-2015)
    Given a Euclidean Jordan algebra (V,o,〈.,.〉) with the (corresponding) symmetric cone K, a linear transformation L:V→V and qεV, the linear complementarity problem LCP(L,q) is to find a vector xεV such thatxεK, y:=L(x)+qεK and xy=0. To investigate the global uniqueness of solutions in the setting of Euclidean Jordan algebras, the P-property and its variants of a linear transformation were introduced in Gowda et al. (2004) [3] and it is shown that if LCP(L,q) has a unique solution for all qεV, then L has the P-property but the converse is not true in general. In the present paper, when (V,o,〈,〉) is the Jordan spin algebra, we show that LCP(L,q) has a unique solution for all qεV if and only if L has the P-property and L is positive semidefinite on the boundary of K.
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    Publication
    Characterization of p-property for some z-transformations on positive semidefinite cone
    (01-01-2011)
    The P-property of the following two Z-transformations with respect to the positive semidefinite cone is characterized: (i) I-S, where S: Sn×n→Sn×n is a nilpotent linear transformation, (ii) I-L-1 A, where LA is the Lyapunov transformation defined on Sn×n by LA(X) = AX + XAT. (Here Sn×n denotes the space of all symmetric n×n matrices and I is the identity transformation.).