On partial calmness for bilevel programming problem with a linear lower-level problem
Abstract
Numerous publications are devoted to bilevel programming problems. Despite a seemingly simple statement these problems are considerably difficult for numerical solving, and a significant part of research in the field of bilevel programming is devoted to identifying particular subsets of problems that allow for a numerical solution. One of such subsets consists of bilevel problems that possess the partial calmness property. Global partial calmness of bilevel programming problems with a linear lower-level problem is proven in this article.
About the Authors
D. E. Berezhnov
Belarusian state university of informatics and radioelectronics
Belarus
Belarus
L. I. Minchenko
Belarusian state university of informatics and radioelectronics
Belarus
Belarus
References
1. Dempe S. Foundations of Bilevel programming. Dordrecht: Kluwer Academic Publishers, 2002. 304 p.
2. Bard J.F. Practical Bilevel Optimization. Dordrecht: Kluwer Academic Publishers, 1998. 476 p.
3. Ye J.J., Zhu D.L. Optimality conditions for bilevel programming problems // Optimization. 1995. № 33. P. 9-27.
4. Dempe S., Zemkoho A.B. Bilevel programming: reformulations, constraint qualifications and optimality conditions // Math. Program. 2013. № 138. P. 447-473
5. Федоров В.В. Численные методы максимина. М., Наука, 1979. 278 с.
6. Пшеничный Б.Н. Выпуклый анализ и экстремальные задачи. М., Наука, 1980. 319 с.
7. Кларк Ф. Оптимизация и негладкий анализ. М., Наука, 1988. 280 с.
Review
For citations:
Berezhnov D.E., Minchenko L.I. On partial calmness for bilevel programming problem with a linear lower-level problem. Doklady BGUIR. 2017;(5):89-92. (In Russ.)
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