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On the Lipschitzian property in linear complementarity problems over symmetric cones. (English) Zbl 1218.90196
Summary: Let V be a Euclidean Jordan algebra with symmetric cone K. We show that if a linear transformation L on V has the Lipschitzian property and the linear complementarity problem LCP(L,q) over K has a solution for every invertible qV, then L(c),c>0 for all primitive idempotents c in V. We show that the converse holds for Lyapunov-like transformations, Stein transformations and quadratic representations. We also show that the Lipschitzian Q-property of the relaxation transformation R A on V implies that A is a P-matrix.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
17C55Finite dimensional structures
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