Feasibility and structural feature on monotone second-order cone linear complementarity problems in Hilbert space

Abstract

Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q∈H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.

Keywords

second-order cone linear complementarity / Jordan frame / Jordan product / Lorentz cone / adjoint operator

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