Application of topological degree theory to semi-definite complementarity problem
V. A. Bulavsky, George Isac, Vyacheslav V. Kalashnikov · Optimization · 2001
The topological degree theory is applied to study the problem of existence of solutions to the semi-definite complementarity problem (SDCP). A notion of an exceptional family of matrices is introduced, and assertions of a non-strict alternative type are obtained. Namely, for a continuous mapping, there exists at least one of the following two items: either a solution to the SDCP, or an exceptional family of matrices. Hence, if there is no exceptional family, then at least one solution exists