On the Guignard constraint qualification for mathematical programs with equilibrium constraints

Optimization

Volumn 54, Issue 6, 2005, Pages 517-534

  Flegel, Michael L ^a   Kanzow, Christian ^a  

^a UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

Guignard constraint qualification; Mathematical programs with equilibrium constraints; Strong stationarity

Indexed keywords

EID: 30944445425     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331930500342591     Document Type: Article

References (24)

1. Bazaraa, M.S. and Shetty, C.M., 1976, Foundations of Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 122 (Berlin: Springer-Verlag, New York: Heidelberg).
2. Chen, Y. and Florian, M., 1995, The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Optimization, 32, 193-209.
3. Facchinei, F., Jiang, H. and Qi, L., 1999, A smoothing method for mathematical programs with equilibrium constraints. Mathematical Programming, 85, 107-134.
4. Flegel, M.L. and Kanzow, C., 2002, An Abadie-type constraint qualification for mathematical programs with equilibrium constraints (Würzburg: Institute of Applied Mathematics and Statistics, University of Würzburg (preprint)).
5. Flegel, M.L. and Kanzow, C., 2003, A Fritz John approach to first order optimality conditions for mathematical programs with equilibrium constraints. Optimization, 52, 277-286.
6. Flegel, M.L. and Kanzow, C., 2005, Abadie-type constraint qualification for mathematical programs with equilibrium constraints. Journal of Optimization Theory and Applications, 124 (to appear).
7. Fukushima, M. and Tseng, P., 2002, An implementable active-set algorithm for computing a B-stationary point of a mathematical program with linear complementarity constraints. SIAM Journal on Optimization, 12, 724-739.
8. Gould, F.J. and Tolle, J.W., 1971, A necessary and sufficient qualification for constrained optimization. SIAM Journal on Applied Mathematics, 20, 164-172.
9. Guignard, M., 1969, Generalized Kuhn-Tuckcr conditions for mathematical programming problems in a Banach space. SIAM Journal on Control, 7, 232-241.
10. Hu, X.M. and Ralph, D., 2000, Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints, tech. rep. (England: Judge Institute of Management Studies, University of Cambridge).
11. Kyparisis, J., 1985, On uniqueness of Kuhn-Tucker multipliers in nonlinear programming. Mathematical Programming, 32, 242-246.
12. Luo, Z.-Q., Pang, J.-S, and Ralph, D., 1996, Mathematical Programs with Equilibrium Constraints (Cambridge, UK: Cambridge University Press).
13. Outrata, J.V., 1999, Optimality conditions for a class of mathematical programs with equilibrium constraints. Mathematics of Operations Research, 24, 627-644.
14. Outrata, J.V., 2000, A generalized mathematical program with equilibrium constraints. SIAM Journal of Control and Optimization, 38, 1623-1638.
15. Pang, J.-S. and Fukushima, M., 1999, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints. Computational Optimization and Applications, 13, 111-136.
16. Peterson, D.W., 1973, A review of constraint qualifications in finite-dimensional spaces. SIAM Review, 15, 639-654.
17. Rockafellar, R.T., 1970, Convex Analysis (Princeton, New Jersey: Princeton University Press).
18. Scheel, H. and Scholtes, S., 2000, Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Mathematics of Operations Research, 25, 1-22.
19. Scholtes, S., 2001, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. SIAM Journal on Optimization, 11, 918-936.
20. Spellucci, P., 1993, Numerische Verfahren der Nichtlinearen Optimierung, Internationale Schriftenreihe zur Numerischen Mathematik (Basel/Boston/Bcrlin: Lehrbuch, Birkhäuser).
21. Stoer, J. and Witzgall, C., 1970, Convexity and Optimization in Finite Dimensions I, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Vol. 163 (Berlin/Heidelberg/New York: Springer-Verlag).
22. Ye, J.J., 2000, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints. SIAM Journal on Optimization, 10, 943-962.
23. Ye, J.J., 2005, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. Journal on Mathematical Analysis and Applications, 307, 350-369.
24. Ye, J.J. and Zhu, D.L., 1995, Optimality conditions for bilevel programming problems. Optimization, 33, 9-27.