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

Authors:
X. D. Chen;D. Sun;J. Sun
Affiliations:
Department of Applied Mathematics, Tongji University, Shanghai, China. chenxiongda@yahoo.com;Department of Mathematics, National University of Singapore, Republic of Singapore. matsundf@nus.edu.sg;SMA and Department of Decision Sciences, National University of Singapore, Republic of Singapore. jsun@nus.edu.sg
Venue:
Computational Optimization and Applications
Year:
2003

Citing 9
Cited 22

Stable monotone variational inequalities

Mathematical Programming: Series A and B
A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
Pseudomonotone variational inequality problems: existence of solutions

Mathematical Programming: Series A and B
Linear systems in Jordan algebras and primal-dual interior-point algorithms

Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Solving variational inequality problems via smoothing-nonsmooth reformulations

Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
Smoothing Functions for Second-Order-Cone Complementarity Problems

SIAM Journal on Optimization
Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results

SIAM Journal on Optimization
Semismooth Matrix-Valued Functions

Mathematics of Operations Research
Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP

Mathematical Programming: Series A and B

Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems

Mathematics of Operations Research
A matrix-splitting method for symmetric affine second-order cone complementarity problems

Journal of Computational and Applied Mathematics
Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

Mathematics of Operations Research
A multisplitting method for symmetrical affine second-order cone complementarity problem

Computers & Mathematics with Applications
A descent method for a reformulation of the second-order cone complementarity problem

Journal of Computational and Applied Mathematics
A globally convergent method based on Fischer-Burmeister operators for solving second-order cone constrained variational inequality problems

Computers & Mathematics with Applications
A matrix-splitting method for symmetric affine second-order cone complementarity problems

Journal of Computational and Applied Mathematics
A semismooth Newton method for SOCCPs based on a one-parametric class of SOC complementarity functions

Computational Optimization and Applications
Penalized complementarity functions on symmetric cones

Journal of Global Optimization
A one-parametric class of merit functions for the second-order cone complementarity problem

Computational Optimization and Applications
Smoothing algorithms for complementarity problems over symmetric cones

Computational Optimization and Applications
A non-interior-point smoothing method for variational inequality problem

Journal of Computational and Applied Mathematics
A generalized Newton method for absolute value equations associated with second order cones

Journal of Computational and Applied Mathematics
Solvability of Newton equations in smoothing-type algorithms for the SOCCP

Journal of Computational and Applied Mathematics
A modified smoothing and regularized Newton method for monotone second-order cone complementarity problems

Computers & Mathematics with Applications
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones

SIAM Journal on Optimization
The penalized Fischer-Burmeister SOC complementarity function

Computational Optimization and Applications
A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation

Journal of Global Optimization
A proximal point algorithm for the monotone second-order cone complementarity problem

Computational Optimization and Applications
The SC1 property of the squared norm of the SOC Fischer-Burmeister function

Operations Research Letters
The solution set structure of monotone linear complementarity problems over second-order cone

Operations Research Letters
An alternating direction method for second-order conic programming

Computers and Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

Two results on the second-order-cone complementarity problem are presented. We show that the squared smoothing function is strongly semismooth. Under monotonicity and strict feasibility we provide a new proof, based on a penalized natural complementarity function, for the solution set of the second-order-cone complementarity problem being bounded. Numerical results of squared smoothing Newton algorithms are reported.