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On an interconnection between the Lipschitz continuity of the solution map and the positive principal minor property in linear complementarity problems over Euclidean Jordan algebras. (English) Zbl 1138.90033
Let V be an Euclidean Jordan algebra, K be a symmetric cone in V, L:VV be a linear transformation and qV. The linear complementary problem associated to L and q, LCP(L,q), prescribes finding xV such that xK, Lx+qK and x,Lx+q=0. It is well known that when V= n and L is a real matrix, LCP(L,q) has a unique solution for all q n , iff all the principal minors of L are positive. In this case the solution map of the LCP(L,q) is well defined and Lipschitz continuous in n . The main result of this paper establishes one direction of the analogous property in the general case: if the solution map is Lipschitz continuous and if L has the Q-property, then L has the positive principal minor property.
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
17C30Automorphisms and other operators on Jordan algebras
17C50Jordan structures associated with other structures