A generalized Jacobian based Newton method for semismooth block-triangular system of equations

The Josephy–newton Method for Semismooth Generalized Equations and Semismooth Sqp for Optimization

While generalized equations with differentiable single-valued base mappings and the associated Josephy–Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush-Kuhn-Tucker optimality systems). We introduce for the general semismooth case appropriate notion...

A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs

We consider a regularization method for nonlinear complementarity problems with F being a P0-function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed b...

A nonmonotone semismooth inexact Newton method

In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems. Finally, we show how we can apply these strategies in the variational inequalities context and we prese...

A Direct Method for Numerically Solving Integral Equations System Using Orthogonal Triangular Functions

[Article] Hybrid Newton-type method for a class of semismooth equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite difference Newton method to a inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear o...