THE GENERALIZED ORDER LINEAR COMPLEMENTARITY-PROBLEM

The generalized order linear complementarity problem (in the setting of a finite dimensional vector lattice) is the problem of finding a solution to the piecewise-linear system x AND (M1x + q1 ) AND (M2x + q2) AND ... AND (M(k)x + q(k)) = 0, where M(i)'s are linear transformations and q(i)'s are vectors. This problem is equivalent to the generalized linear complementarity problem considered by Cottle and Dantzig [J. Combin. Theory, 8 (1970), pp- 79-90.]. Using degree theory, a comprehensive analysis of existence, uniqueness, and stability aspects of this problem is presented.