Regularization method for stochastic mathematical programs with complementarity constraints

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 11, Issue 2, 2005, Pages 252-265

  Lin, Gui Hua ^a,b   Fukushima, Masao ^b  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Benjamin Ono equation; Dispersive equation; Exact controllability; Stabilization

Indexed keywords

CONSTRAINT THEORY; OPTIMIZATION; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

MANGASARIAN-FROMOVITZ CONSTRAINT QUALIFICATION; REGULARIZATION; S-STATIONARITY; STOCHASTIC MATHEMATICAL PROGRAM WITH EQUILIBRIUM CONSTRAINTS;

STOCHASTIC PROGRAMMING;

EID: 30844467532     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2005005     Document Type: Article

References (12)

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