A proximal point algorithm for the monotone second-order cone complementarity problem

Authors:
Jia Wu;Jein-Shan Chen
Affiliations:
School of Mathematical Sciences, Dalian University of Technology, Dalian, China 116024;Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan 11677
Venue:
Computational Optimization and Applications
Year:
2012

Citing 13
Cited 0

A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
A semismooth equation approach to the solution of nonlinear complementarity problems

Mathematical Programming: Series A and B
Solution of monotone complementarity problems with locally Lipschitzian functions

Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Smoothing Functions for Second-Order-Cone Complementarity Problems

SIAM Journal on Optimization
The Proximal Point Algorithm with Genuine Superlinear Convergence for the Monotone Complementarity Problem

SIAM Journal on Optimization
Complementarity Functions and Numerical Experiments on Some Smoothing Newton Methods for Second-Order-Cone Complementarity Problems

Computational Optimization and Applications
A Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems

SIAM Journal on Optimization
A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems

SIAM Journal on Optimization
Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions

Mathematical Programming: Series A and B
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem

Mathematical Programming: Series A and B
Cartesian P-property and Its Applications to the Semidefinite Linear Complementarity Problem

Mathematical Programming: Series A and B
Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones

SIAM Journal on Optimization
On the Local Convergence of Semismooth Newton Methods for Linear and Nonlinear Second-Order Cone Programs Without Strict Complementarity

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm is verified to have global and superlinear convergence properties. For the purpose of solving the subproblems efficiently, we introduce a generalized Newton method and show that only one Newton step is eventually needed to obtain a desired approximate solution that approximately satisfies the appropriate criterion under mild conditions. Numerical comparisons are also made with the derivative-free descent method used by Pan and Chen (Optimization 59:1173---1197, 2010), which confirm the theoretical results and the effectiveness of the algorithm.