Two approaches for solving mathematical programs withsecond-order cone complementarity constraints

Xi-De Zhu; Li-Ping Pang; Gui-Hua Lin

doi:10.3934/jimo.2015.11.951

Article Contents

2015, Volume 11, Issue 3: 951-968. Doi: 10.3934/jimo.2015.11.951

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

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

Received: July 31, 2013

Revised: May 31, 2014

Published: June 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C30, 90C33; Secondary: 90C46.

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