Smoothing Functions for Second-Order-Cone Complementarity Problems

Authors:
Masao Fukushima;Zhi-Quan Luo;Paul Tseng
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2002

Citing 0
Cited 39

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

Computational Optimization and Applications
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
Second-order cone programming formulations for robust multiclass classification

Neural Computation
Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

Mathematics of Operations Research
A Newton's method for perturbed second-order cone programs

Computational Optimization and Applications
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 one-step smoothing Newton method for second-order cone programming

Journal of Computational and Applied Mathematics
A smoothing method for second order cone complementarity problem

Journal of Computational and Applied Mathematics
Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones

Journal of Computational and Applied Mathematics
Some characterizations for SOC-monotone and SOC-convex functions

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

Computational Optimization and Applications
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
An Explicit Exchange Algorithm For Linear Semi-Infinite Programming Problems With Second-Order Cone Constraints

SIAM Journal on Optimization
A Singular Value Thresholding Algorithm for Matrix Completion

SIAM Journal on Optimization
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones

SIAM Journal on Optimization
A class of nonlinear Lagrangians for nonconvex second order cone programming

Computational Optimization and Applications
A nonsmooth algorithm for cone-constrained eigenvalue problems

Computational Optimization and Applications
The penalized Fischer-Burmeister SOC complementarity function

Computational Optimization and Applications
A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics

Proceedings of the 2011 SIGGRAPH Asia Conference
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
Neural networks for solving second-order cone constrained variational inequality problem

Computational Optimization and Applications
Stationary point conditions for the FB merit function associated with symmetric cones

Operations Research Letters
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
Recurrent neural networks for solving second-order cone programs

Neurocomputing
Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets

Journal of Global Optimization
Nonsingularity Conditions for the Fischer-Burmeister System of Nonlinear SDPs

SIAM Journal on Optimization
A second order cone complementarity approach for the numerical solution of elastoplasticity problems

Computational Mechanics
An alternating direction method for second-order conic programming

Computers and Operations Research
Inverse dynamic hair modeling with frictional contact

ACM Transactions on Graphics (TOG)
A smoothed NR neural network for solving nonlinear convex programs with second-order cone constraints

Information Sciences: an International Journal

Quantified Score

Hi-index	0.01

Visualization

Abstract

Smoothing functions have been much studied in the solution of optimization and complementarity problems with nonnegativity constraints. In this paper, we extend smoothing functions to problems in which the nonnegative orthant is replaced by the direct product of second-order cones. These smoothing functions include the Chen--Mangasarian class and the smoothed Fischer--Burmeister function. We study the Lipschitzian and differential properties of these functions and, in particular, we derive computable formulas for these functions and their Jacobians. These properties and formulas can then be used to develop and analyze noninterior continuation methods for solving the corresponding optimization and complementarity problems. In particular, we establish the existence and uniqueness of the Newton direction when the underlying mapping is monotone.