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

Authors:
Marek J. mietański
Affiliations:
Department of Numerical Methods, University of Lodz, ul. Banacha 22, 90-238 Lodz, Poland
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 10
Cited 1

Newton's method for the nonlinear complementarity problem: a B-differentiable equation problem

Mathematical Programming: Series A and B
A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations

Mathematics of Operations Research
A parameterized Newton method and a quasi-Newton method for nonsmooth equations

Computational Optimization and Applications
Inexact Newton methods for solving nonsmooth equations

Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Approximate Newton methods for nonsmooth equations

Journal of Optimization Theory and Applications
Engineering and Economic Applications of Complementarity Problems

SIAM Review
Inexact-Newton methods for semismooth system of equations with block-angular structure

Journal of Computational and Applied Mathematics
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems

SIAM Journal on Optimization

Computation of generalized differentials in nonlinear complementarity problems

Computational Optimization and Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

This paper will consider the problem of solving the nonlinear system of equations with block-triangular structure. A generalized block Newton method for semismooth sparse system is presented and a locally superlinear convergence is proved. Moreover, locally linear convergence of some parameterized Newton method is shown.