Some properties of the bilevel programming problem
- J. F. Bard
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The purpose of this paper is to elaborate on the difficulties accompanying the development of efficient algorithms for solving the bilevel programming problem (BLPP). We begin with a pair of examples showing that, even under the best of circumstances, solutions may not exist. This is followed by a proof that the BLPP is NP-hard.
- Bard, J. F.,Optimality Conditions for the Bilevel Programming Problem, Naval Research Logistics Quarterly, Vol. 31, pp. 13–26, 1984.
- Hasen, P., Jaumard, B., andSavard, G.,A Variable Elimination Algorithm for Bilevel Programming, RUTCOR Research Report RRR-17-89, Rutgers University, New Brunswick, New Jersey, 1989.
- Jeroslow, R. G.,The Polynomial Hierarchy and a Simple Model for Competitive Analysis, Mathematical Programming, Vol. 32, pp. 146–164, 1985.
- Hogan, W. W.,Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591–603, 1973.
- Garey, M. R. andJohnson, D. S.,Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, New York, New York, 1979.
- Ben-Ayed, O., andBlair, C. E.,Computational Difficulties of Bilevel Programming, Working Paper WP-1432, College of Commerce and Business Administration, University of Illinois, Urbana, Illinois, 1988.
- Some properties of the bilevel programming problem
Journal of Optimization Theory and Applications
Volume 68, Issue 2 , pp 371-378
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- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Bilevel programming
- Stackelberg games
- computational complexity
- Industry Sectors
- J. F. Bard (1)
- Author Affiliations
- 1. Operations Research Group, Department of Mechanical Engineering, University of Texas, Austin, Texas