A Globally Convergent Successive Approximation Method for Severely Nonsmooth Equations

Authors:
Liqun Qi;Xiaojun Chen
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1995

Citing 0
Cited 16

A primal-dual algorithm for minimizing a sum of Euclidean norms

Journal of Computational and Applied Mathematics
Smoothing functions and smoothing Newton method for complementarity and variational inequality problems

Journal of Optimization Theory and Applications
Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems

Computational Optimization and Applications
A Global Linear and Local Quadratic Continuation Smoothing Method for Variational Inequalities with Box Constraints

Computational Optimization and Applications
Applications of smoothing methods in numerical analysis and optimization

Focus on computational neurobiology
An entropic regularization approach for mathematical programs with equilibrium constraints

Computers and Operations Research
A Smoothing Newton Method for Semi-Infinite Programming

Journal of Global Optimization
A norm descent BFGS method for solving KKT systems of symmetric variational inequality problems

Optimization Methods & Software
A new hybrid method for nonlinear complementarity problems

Computational Optimization and Applications
Foreword

Computational Optimization and Applications
Generalized Newton-iterative method for semismooth equations

Numerical Algorithms
Smoothing Nonlinear Conjugate Gradient Method for Image Restoration Using Nonsmooth Nonconvex Minimization

SIAM Journal on Imaging Sciences
Recursive approximation of the high dimensional max function

Operations Research Letters
A perturbed version of an inexact generalized Newton method for solving nonsmooth equations

Numerical Algorithms
A quasisecant method for solving a system of nonsmooth equations

Computers & Mathematics with Applications
A fixed-point method for a class of super-large scale nonlinear complementarity problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a globally convergent successive approximation method for solving $F(x)=0$ where $F$ is a continuous function. At each step of the method, $F$ is approximated by a smooth function $f_{k},$ with $\pa f_{k}-F\pa \rightarrow 0$ as $k \rightarrow \infty$. The direction $-f'_{k}(x_{k})^{-1}F(x_{k})$ is then used in a line search on a sum of squares objective. The approximate function $f_k$ can be constructed for nonsmooth equations arising from variational inequalities, maximal monotone operator problems, nonlinear complementarity problems, and nonsmooth partial differential equations. Numerical examples are given to illustrate the method.