A regularized smoothing Newton-type algorithm for quasi-variational inequalities

Abstract

This paper is concerned with developing an efficient regularized smoothing Newton-type algorithm for quasi-variational inequalities. The proposed algorithm takes the advantage of newly introduced smoothing functions and a non-monotone line search strategy. It is proved to be globally and locally superlinearly/quadratically convergent under suitable assumptions. Numerical results demonstrate that the algorithm generally outperforms the existing interior point method and semismooth method (Facchinei, et al. 2014).