# American Institute of Mathematical Sciences

July  2015, 11(3): 733-746. doi: 10.3934/jimo.2015.11.733

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

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

Received  September 2013 Revised  June 2014 Published  October 2014

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.
Citation: Shuang Chen, Li-Ping Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial & Management Optimization, 2015, 11 (3) : 733-746. doi: 10.3934/jimo.2015.11.733
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