An inexact semismooth Newton method  for variational inequality with      symmetric cone constraints

Shuang Chen; Li-Ping Pang; Dan Li

doi:10.3934/jimo.2015.11.733

Article Contents

2015, Volume 11, Issue 3: 733-746. Doi: 10.3934/jimo.2015.11.733

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An inexact semismooth Newton method for variational inequality with symmetric cone constraints

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning
2.
Information and Engineering College, Dalian University, Dalian 116622

Received: August 31, 2013

Revised: May 31, 2014

Published: June 2015

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Abstract

In this paper, we consider using the inexact nonsmooth Newton method to efficiently solve the symmetric cone constrained variational inequality (VISCC) problem. It red provides a unified framework for dealing with the variational inequality with nonlinear constraints, variational inequality with the second-order cone constraints, and the variational inequality with semidefinite cone constraints. We get convergence of the above method and apply the results to three special types symmetric cones.

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Mathematics Subject Classification: Primary: 90C15, 65C05; Secondary: 49J52, 49M27, 49M37.

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