Regularization method for stochastic mathematical programs with complementarity constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 252-265.

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.

DOI : 10.1051/cocv:2005005
Classification : 90C30, 90C33
Mots-clés : stochastic mathematical program with equilibrium constraints, S-stationarity, Mangasarian-Fromovitz constraint qualification 
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Lin, Gui-Hua; Fukushima, Masao. Regularization method for stochastic mathematical programs with complementarity constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 252-265. doi : 10.1051/cocv:2005005. https://www.numdam.org/articles/10.1051/cocv:2005005/

[1] J.R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer, New York (1997). | MR | Zbl

[2] J.F. Bonnans and A. Shapiro, Optimization problems with perturbations: A guided tour. SIAM Rev. 40 (1998) 228-264. | Zbl

[3] Y. Chen and M. Florian, The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions. Optimization 32 (1995) 193-209. | Zbl

[4] R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, New York, NY (1992). | MR | Zbl

[5] K. Jittorntrum, Solution point differentiability without strict complementarity in nonlinear programming. Math. Program. Stud. 21 (1984) 127-138. | Zbl

[6] P. Kall and S.W. Wallace, Stochastic Programming. John Wiley & Sons, Chichester (1994). | MR | Zbl

[7] G.H. Lin, X. Chen and M. Fukushima, Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints. Technical Report 2003-006, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2003).

[8] G.H. Lin and M. Fukushima, A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms. Technical Report 2003-010, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan (2003).

[9] Z.Q. Luo, J.S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK (1996). | MR | Zbl

[10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992). | MR | Zbl

[11] M. Patriksson and L. Wynter, Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. 25 (1999) 159-167. | Zbl

[12] H.S. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000) 1-22. | Zbl

  • Lin, G.-H.; Chen, X.; Fukushima, M. New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC, Optimization, Volume 56 (2007) no. 5-6, p. 641 | DOI:10.1080/02331930701617320
  • Fukushima, Masao, Second International Conference on Informatics Research for Development of Knowledge Society Infrastructure (ICKS'07) (2007), p. 87 | DOI:10.1109/icks.2007.30
  • FUKUSHIMA, MASAO HOW TO DEAL WITH UNCERTAINTY IN OPTIMIZATION — SOME RECENT ATTEMPTS, International Journal of Information Technology Decision Making, Volume 05 (2006) no. 04, p. 623 | DOI:10.1142/s0219622006002192
  • Lin, Gui-Hua; Fukushima, Masao New reformulations for stochastic nonlinear complementarity problems, Optimization Methods and Software, Volume 21 (2006) no. 4, p. 551 | DOI:10.1080/10556780600627610

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