The Generalized Order Linear Complementarity Problem

摘要: The generalized order linear complementarity problem (in the setting of a finite dimensional vector lattice) is finding solution to piecewise-linear system $$ x \wedge (M_{1}x + q_{l}) (M_{2}x q_{2}) \cdots (M_{k}x q_{k}) = 0, where $M_i$'s are transformations and $q_i$'s vectors. This equivalent genaralized considered by Cottle Dantzig [J. Combin. Theory, 8 (1970), pp. 79-90.]. Using degree theory, comprehensive analysis existence, uniqueness, stability aspects this presented.