A variant smoothing Newton method for P0-NCP based on a new smoothing function

Authors:
Jian Zhang;Ke-Cun Zhang
Affiliations:
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China;Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 11
Cited 1

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
A non-interior-point continuation method for linear complementarity problems

SIAM Journal on Matrix Analysis and Applications
Engineering and Economic Applications of Complementarity Problems

SIAM Review
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

Mathematics of Computation
Beyond Monotonicity in Regularization Methods for Nonlinear Complementarity Problems

SIAM Journal on Control and Optimization
Improving the convergence of non-interior point algorithms for nonlinear complementarity problems

Mathematics of Computation
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 Regularized Smoothing Newton Method for Box Constrained Variational Inequality Problems with P0-Functions

SIAM Journal on Optimization
Smooth Approximations to Nonlinear Complementarity Problems

SIAM Journal on Optimization
The convergence of a one-step smoothing Newton method for P0-NCP based on a new smoothing NCP-function

Journal of Computational and Applied Mathematics

A smoothing inexact Newton method for nonlinear complementarity problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we present a new one-step smoothing Newton method proposed for solving the non-linear complementarity problem with P"0-function based on a new smoothing NCP-function. We adopt a variant merit function. Our algorithm needs only to solve one linear system of equations and perform one line search per iteration. It shows that any accumulation point of the iteration sequence generated by our algorithm is a solution of P"0-NCP. Furthermore, under the assumption that the solution set is non-empty and bounded, we can guarantee at least one accumulation point of the generated sequence. Numerical experiments show the feasibility and efficiency of the algorithm.