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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

Xi-De Zhu 1, , Li-Ping Pang 2, and  Gui-Hua Lin 3,

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.
Keywords: convergence., Clarke-type stationarity, smoothing function, MPSOCC, relaxation.
Mathematics Subject Classification: Primary: 90C30, 90C33; Secondary: 90C4.
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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show all references

References:
[1]

Mathematical Programming, 95 (2003), 3-51. doi: 10.1007/s10107-002-0339-5.  Google Scholar

[2]

Mathematical Programming, 101 (2004), 95-117. doi: 10.1007/s10107-004-0538-3.  Google Scholar

[3]

Pacific Journal of Optimization, 8 (2012), 33-74.  Google Scholar

[4]

Computational Optimization and Applications, 25 (2003), 39-56. doi: 10.1023/A:1022996819381.  Google Scholar

[5]

Optimization, 32 (1995), 193-209. doi: 10.1080/02331939508844048.  Google Scholar

[6]

Oxford Mathematical Monographs, Oxford University Press, New York, 1994.  Google Scholar

[7]

Proceedings of the ICKS'04, IEEE Computer Society, 2004 (2004), 206-213. doi: 10.1109/ICKS.2004.1313426.  Google Scholar

[8]

SIAM Journal on Optimization, 12 (2001), 436-460. doi: 10.1137/S1052623400380365.  Google Scholar

[9]

SIAM Journal on Optimization, 15 (2005), 593-615. doi: 10.1137/S1052623403421516.  Google Scholar

[10]

Set-Valued and Variational Analysis, 22 (2014), 59-78. doi: 10.1007/s11228-013-0250-7.  Google Scholar

[11]

Cambridge University Press, Cambridge, United Kingdom, 1996. doi: 10.1017/CBO9780511983658.  Google Scholar

[12]

Kluwer Academic Publisher, Dordrect, The Netherlands, 1998. doi: 10.1007/978-1-4757-2825-5.  Google Scholar

[13]

Set-Valued Analysis, 16 (2008), 999-1014. doi: 10.1007/s11228-008-0092-x.  Google Scholar

[14]

Optimization, 60 (2011), 113-128. doi: 10.1080/02331934.2010.541458.  Google Scholar

[15]

Pacific Journal of Optimization, 9 (2013), 345-372.  Google Scholar

[16]

SIAM Journal on Optimizaion, 7 (1997), 481-507. doi: 10.1137/S1052623493257344.  Google Scholar

[17]

Set-Valued Analysis, 19 (2011), 609-646. doi: 10.1007/s11228-011-0190-z.  Google Scholar

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