Equivalence of Linear Complementarity Problems and Linear Programs in Vector Lattice Hilbert Spaces.

摘要

Let X be a vector lattice Hilbert space with dual X*. Let M be a continuous linear mapping of X onto X*. Let p, q elements of X* with p > 0r 0. Considered is the relationship between the linear complementarity problem: Find x elements of X such that x > or = 0, Mx + q > or = 0, (x, Mx + q) = 0, and the linear programming problem: Find x element of X which minimizes (x,p) subject to > or = 0, Mx + q > or = 0. (Author)