Stochastic mathematical programs with equilibrium constraints

Operations Research Letters

Volumn 25, Issue 4, 1999, Pages 159-167

  Patriksson, Michael ^a   Wynter, Laura ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF VERSAILLES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

BILEVEL PROGRAMMING; STOCHASTIC PROGRAMMING; UPPER-LEVEL OBJECTIVE FUNCTIONS; VARIATIONAL INEQUALITIES;

OPERATIONS RESEARCH;

EID: 0033339162     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(99)00052-8     Document Type: Article

References (23)

1. J.R. Birge, X. Chen, L. Qi, Z. Wei, A stochastic Newton method for stochastic quadratic programs with recourse, Technical Report, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 1995.
2. J.R. Birge, F. Louveaux, Stochastic Programming, Springer, New York, NY, 1997.
3. S. Christiansen, M. Patriksson, L. Wynter, Stochastic bilevel programming in structural optimization, Technical Report, PRISM, Computer Science Department, Université de Versailles, Versailles, France, 1999, submitted for publication.
4. Facchinei F., Jiang H., Qi L. A smoothing method for mathematical programs with equilibrium constraints. Math. Programming. 85:1999;107-134.
5. Facchinei F., Soares J. A new merit function for nonlinear complementarity problems and a related algorithm. SIAM J. Optim. 7:1997;225-247.
6. A.V. Fiacco, Optimal value continuity and differential stability bounds under the Mangasarian-Fromovitz constraint qualification, in: A.V. Fiacco (Ed.), Mathematical Programming with Data Perturbations II, Marcel Dekker, New York, NY, 1983, pp. 65-90.
7. Geoffrion A.M. Elements of large-scale mathematical programming. Management Sci. 16:1970;652-691.
8. Hansen P., Jaumard B., Savard G. New branch-and-bound rules for linear bilevel programming. SIAM J. Scientific Statist. Comput. 13:1992;1194-1217.
9. Harker P.T., Choi S.-C. A penalty function approach for mathematical programs with variational inequality constraints. Inform. Decision Technol. 17:1991;41-50.
10. Higle J.L., Sen S. Stochastic decomposition: An algorithm for two stage linear programs with recourse. Math. Oper. Res. 16:1991;650-669.
11. Hogan W.W. Directional derivatives for extremal-value functions with applications to the completely convex case. Oper. Res. 21:1973;188-209.
12. Larsson T., Patriksson M. A class of gap functions for variational inequalities. Math. Programming. 64:1994;53-79.
13. Z.-Q. Luo, J.-S. Pang, D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, Cambridge, UK, 1996.
14. Marcotte P. Network design problem with congestion effects: A case of bilevel programming. Math. Programming. 34:1986;142-162.
15. Marcotte P., Zhu D. Exact and inexact penalty methods for the generalized bilevel programming problem. Math. Programming. 74:1996;141-157.
16. K. Marti (Ed.), Structural reliability and stochastic structural optimization, (special issue) Math. Methods Oper. Res. 46(3) (1997).
17. Outrata J., Zowe J. A numerical approach to optimization problems with variational inequality constraints. Math. Programming. 68:1995;105-130.
18. Robinson S.M. Strongly regular generalized equations. Math. Oper. Res. 5:1980;43-62.
19. Robinson S.M. An implicit-function theorem for a class of nonsmooth functions. Math. Oper. Res. 16:1991;282-309.
20. Rockafellar R.T., Wets R.J.-B. A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming. Math. Programming Study. 28:1986;63-93.
21. K. Shimizu, Y. Ishizuka, J. Bard, Nondifferentiable and Two-Level Mathematical Programming, Kluwer Academic Publishers, Boston, MA, 1997.
22. R.J.-B. Wets, Stochastic programming, in: Handbooks in Operations Research and Management Science, G.L. Nemhauser, A.H.G. Rinnooy Kan, M.J. Todd (Eds.), Optimization, Vol. 1, North-Holland, Amsterdam, 1989, pp. 573-629 (Chapter VIII).
23. Zhang R. Problems of hierarchical optimization in finite dimension. SIAM J. Optim. 4:1994;521-536.