A non-interior continuation algorithm for the CP based on a generalized smoothing function

Authors:
Li-Yong Lu;Wei-Zhe Gu
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 21
Cited 2

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

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

SIAM Journal on Matrix Analysis and Applications
Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems

Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Solution of monotone complementarity problems with locally Lipschitzian functions

Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A Comparison of Large Scale Mixed Complementarity Problem Solvers

Computational Optimization and Applications
On unconstrained and constrained stationary points of the implicit Lagrangian

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

SIAM Review
The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems

Mathematics of Operations Research
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems

Computational Optimization and Applications
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 New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm

SIAM Journal on Optimization
Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP

Mathematical Programming: Series A and B
A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for P0-NCPs

Journal of Computational and Applied Mathematics
A smoothing-type algorithm for solving system of inequalities

Journal of Computational and Applied Mathematics
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems

Optimization Methods & Software
Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems

Journal of Computational and Applied Mathematics
An R-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized Fischer-Burmeister merit function

Journal of Computational and Applied Mathematics
A regularized smoothing-type algorithm for solving a system of inequalities with a P0-function

Journal of Computational and Applied Mathematics
A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities

Journal of Computational and Applied Mathematics

A full-Newton step non-interior continuation algorithm for a class of complementarity problems

Journal of Computational and Applied Mathematics
A fixed-point method for a class of super-large scale nonlinear complementarity problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

Based on the generalized CP-function proposed by Hu et al. [S.L. Hu, Z.H. Huang, J.S. Chen, Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems, J. Comput. Appl. Math. 230 (2009) 69-82], we introduce a smoothing function which is a generalization of several popular smoothing functions. By which we propose a non-interior continuation algorithm for solving the complementarity problem. The proposed algorithm only needs to solve at most one system of linear equations at each iteration. In particular, we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate that the algorithm is effective.