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New reformulations for stochastic nonlinear complementarity problems. (English) Zbl 1113.90110
Summary: We consider the stochastic nonlinear complementarity problem (SNCP). We first formulate the problem as a stochastic mathematical program with equilibrium constraints and then, in order to develop efficient algorithms, we give some reformulations of the problem. Furthermore, based on the reformulations, we propose a smoothed penalty method for solving SNCP. A rigorous convergence analysis is also given.

MSC:
90C15 Stochastic programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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References:
[1] Cottle R. W., The Linear Complementarity Problem (1992)
[2] DOI: 10.1007/s101070050024 · Zbl 0972.90079 · doi:10.1007/s101070050024
[3] DOI: 10.1023/A:1021018421126 · Zbl 1034.91019 · doi:10.1023/A:1021018421126
[4] DOI: 10.1287/moor.1050.0160 · Zbl 1162.90527 · doi:10.1287/moor.1050.0160
[5] Luo Z. Q., Mathematical Programs with Equilibrium Constraints (1996)
[6] Lin, G. H., Chen, X. and Fukushima, M. 2003. ”Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints”. Kyoto, Japan: Kyoto University. Technical Report 2003–2006. Department of Applied Mathematics and Physics, Graduate School of Informatics
[7] Lin G. H., Journal of Industrial and Management Optimization 1 pp 99– (2005) · Zbl 1096.90024 · doi:10.3934/jimo.2005.1.99
[8] DOI: 10.1051/cocv:2005005 · Zbl 1080.90055 · doi:10.1051/cocv:2005005
[9] Shapiro, A. 2004. ”Stochastic mathematical programs with equilibrium constraints. Preprint”. Antalanta, Georgia, USA: Georgia Institute of Technology. School of Industrial and System Engineering
[10] Shapiro, A. and Xu, H. 2005. ”Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. Preprint”. Georgia, USA: Georgia Institute of Technology, Antalanta. School of Industrial and System Engineering
[11] DOI: 10.1137/040608544 · Zbl 1113.90114 · doi:10.1137/040608544
[12] Clarke F. H., Optimization and Nonsmooth Analysis (1990) · Zbl 0696.49002 · doi:10.1137/1.9781611971309
[13] DOI: 10.1007/s10479-004-5024-z · Zbl 1119.90058 · doi:10.1007/s10479-004-5024-z
[14] DOI: 10.1023/A:1024739508603 · Zbl 1033.90086 · doi:10.1023/A:1024739508603
[15] DOI: 10.1287/moor.25.1.1.15213 · Zbl 1073.90557 · doi:10.1287/moor.25.1.1.15213
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