A new continuation method for complementarity problems with uniform P- functions
This paper formulates the (nonlinear) complementarity problem relative to a continuous mapping f as a problem of solving a system of equations defined by a particular mapping F from \(R_+^{2n}\) to \(R^ n_+\times R^ n\). It is shown that when f is a uniform P-function, the mapping F is a homeomorphism of \(R_+^{2n}\) to \(R^ n_+\times R^ n\). This forms the foundation of a continuation method for tracing the solution curve of the one-parameter family of systems of equations \(F(x,y)=tF(x^ 0,y^ 0)\) from an arbitrary point \((x^ 0,y^ 0)\in R_+^{2n}\) and \(t=1\) to \(t=0\).
scientific article; zbMATH DE number 4102834