The Kantorovich theorem for nonlinear complementarity problems (Q1200704)

In this note the following nonlinear complementarity problem is considered: Let \(K=\mathbb{R}^ n_ +\), \(F\in K\to\mathbb{R}^ n\). Find \(x\in K\) such that \(F(x)\geq 0\), \((F(x),x)=0\). This problem is equivalent to the variational inequality: Find \(x\in K\) such that \((F(x),y-x)\geq 0\), \(\forall y\in K\). The authors establish some basic results of the semilocal convergence theory of Newton and quasi-Newton methods for solving the given nonlinear complementarity problem.