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July  2015, 11(3): 951-968. doi: 10.3934/jimo.2015.11.951

## Two approaches for solving mathematical programs with second-order cone complementarity constraints

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 2 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning 3 School of Management, Shanghai University, Shanghai 200444, China

Received  August 2013 Revised  June 2014 Published  October 2014

This paper considers a mathematical program with second-order cone complementarity constrains (MPSOCC). We present two approximation methods for solving the MPSOCC. One employs some smoothing functions to approximate the MPSOCC and the other makes use of some techniques to relax the complementarity constrains in the MPSOCC. We investigate the limiting behavior of both methods. In particular, we show that, under mild conditions, any accumulation point of stationary points of the approximation problems must be a Clarke-type stationary point of the MPSOCC.
Citation: Xi-De Zhu, Li-Ping Pang, Gui-Hua Lin. Two approaches for solving mathematical programs with second-order cone complementarity constraints. Journal of Industrial & Management Optimization, 2015, 11 (3) : 951-968. doi: 10.3934/jimo.2015.11.951
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