Applications of smoothing methods in numerical analysis and optimization

Authors:
Xiaojun Chen
Affiliations:
Department of Mathematics System Science, Hirosaki University, Hirosaki 036-8561, Aomori, Japan
Venue:
Focus on computational neurobiology
Year:
2004

Citing 43
Cited 0

Finite element approximation of a model reaction—diffusion problem with a non-Lipschitz nonlinearity

Numerische Mathematik
A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems

Mathematical Programming: Series A and B
Homotopy continuation methods for nonlinear complementarity problems

Mathematics of Operations Research
Fast algorithms for nonsmooth compact fixed-point problems

SIAM Journal on Numerical Analysis
Normal maps inducted by linear transformations

Mathematics of Operations Research
A new computational algorithm for functional inequality constrained optimization problems

Automatica (Journal of IFAC)
A non-interior-point continuation method for linear complementarity problems

SIAM Journal on Matrix Analysis and Applications
A parameterized Newton method and a quasi-Newton method for nonsmooth equations

Computational Optimization and Applications
A Globally Convergent Successive Approximation Method for Severely Nonsmooth Equations

SIAM Journal on Control and Optimization
A continuation method for monotone variational inequalities

Mathematical Programming: Series A and B
Smoothing methods for convex inequalities and linear complementarity problems

Mathematical Programming: Series A and B
Growth behavior of a class of merit functions for the nonlinear complementarity problem

Journal of Optimization Theory and Applications
A class of smoothing functions for nonlinear and mixed complementarity problems

Computational Optimization and Applications
On finite termination of an iterative method for linear complementarity problems

Mathematical Programming: Series A and B
Some Noninterior Continuation Methods for LinearComplementarity Problems

SIAM Journal on Matrix Analysis and Applications
A Comparison of Large Scale Mixed Complementarity Problem Solvers

Computational Optimization and Applications
Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations

Journal of Computational and Applied Mathematics
A verification method for solutions of nonsmooth equations

Computing
New NCP-functions and their properties

Journal of Optimization Theory and Applications
How to deal with the unbounded in optimization: theory and algorithms

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

Mathematics of Computation
A Globally Convergent Sequential Quadratic Programming Algorithm for Mathematical Programs with Linear Complementarity Constraints

Computational Optimization and Applications
Global and Superlinear Convergence of Inexact Uzawa Methods for Saddle Point Problems with Nondifferentiable Mappings

SIAM Journal on Numerical Analysis
The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems

Mathematics of Operations Research
Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities

Mathematical Programming: Series A and B
Weak Univalence and Connectedness of Inverse Images of Continuous Functions

Mathematics of Operations Research
On Homotopy-Smoothing Methods for Box-Constrained Variational Inequalities

SIAM Journal on Control and Optimization
Beyond Monotonicity in Regularization Methods for Nonlinear Complementarity Problems

SIAM Journal on Control and Optimization
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
Solving variational inequality problems via smoothing-nonsmooth reformulations

Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations

SIAM Journal on Numerical Analysis
A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen--Mangasarian Smoothing Functions

SIAM Journal on Optimization
A Global and Local Superlinear Continuation-Smoothing Method for P0 and R0 NCP or Monotone NCP

SIAM Journal on Optimization
A Smoothing Newton Method for Minimizing a Sum of Euclidean Norms

SIAM Journal on Optimization
On Smoothing Methods for the P0 Matrix Linear Complementarity Problem

SIAM Journal on Optimization
A Regularized Smoothing Newton Method for Box Constrained Variational Inequality Problems with P0-Functions

SIAM Journal on Optimization
Convergence of Newton's Method for Singular Smooth and Nonsmooth Equations Using Adaptive Outer Inverses

SIAM Journal on Optimization
Smooth Approximations to Nonlinear Complementarity Problems

SIAM Journal on Optimization
Jacobian Smoothing Methods for Nonlinear Complementarity Problems

SIAM Journal on Optimization
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints

SIAM Journal on Optimization
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
Newton-type methods for stochastic programming

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a brief view of recent applications of smoothing methods in the area of numerical analysis and optimization. We describe various nonsmooth problems and illustrate how to apply smoothing methods to these problems. We summarize properties of smoothing methods which are useful for the convergence analysis and error estimation of smoothing methods.