Sequential injective algorithm for weakly univalent vector equation : with application to regularized smoothing Newton algorithm (Development of Mathematical Optimization : Modeling and Algorithms)

Abstract

It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this short paper, we first study the global convergence of a sequential injective algorithm for weakly univalent vector equation. Then, we apply the convergence analysis to the regularized smoothing Newton algorithm for mixed nonlinear second-order cone complementarity problems. We prove the global convergence property under the (Cartesian) P_{0} assumption, which is strictly weaker than the original monotonicity assumption.