Hostname: page-component-cb9f654ff-fg9bn Total loading time: 0 Render date: 2025-08-02T01:06:51.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Regularization method for stochasticmathematical programs with complementarity constraints

Published online by Cambridge University Press:  15 March 2005

Gui-Hua Lin  and
Masao Fukushima
Gui-Hua Lin
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; ghlin@amp.i.kyoto-u.ac.jp Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan; fuku@amp.i.kyoto-u.ac.jp
Masao Fukushima
Affiliation:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan; fuku@amp.i.kyoto-u.ac.jp
Get access

Abstract

In this paper, we consider a class of stochasticmathematical programs with equilibrium constraints (SMPECs) thathas been discussed by Lin and Fukushima (2003). Based on areformulation given therein, we propose a regularization methodfor solving the problems. We show that, under a weak condition, anaccumulation point of the generated sequence is a feasible pointof the original problem. We also show that such an accumulationpoint is S-stationary to the problem under additional assumptions.

Keywords

Stochastic mathematical program with equilibriumconstraintsS-stationarityMangasarian-Fromovitz constraintqualification.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 2 , April 2005 , pp. 252 - 265
Copyright
© EDP Sciences, SMAI, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

J.R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer, New York (1997).
Bonnans, J.F. and Shapiro, A., Optimization problems with perturbations: A guided tour. SIAM Rev. 40 (1998) 228–264. CrossRef
Chen, Y. and Florian, M., The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions. Optimization 32 (1995) 193–209. CrossRefPubMed
R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem. Academic Press, New York, NY (1992).
Jittorntrum, K., Solution point differentiability without strict complementarity in nonlinear programming. Math. Program. Stud. 21 (1984) 127–138. CrossRef
P. Kall and S.W. Wallace, Stochastic Programming. John Wiley & Sons, Chichester (1994).
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).
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).
Z.Q. Luo, J.S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK (1996).
H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992).
Patriksson, M. and Wynter, L., Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. 25 (1999) 159–167. CrossRef
Scheel, H.S. and Scholtes, S., Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000) 1–22. CrossRef