期刊
OPTIMIZATION
卷 63, 期 4, 页码 505-533出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2012.696641
关键词
optimization and variational analysis; optimality conditions; pessimistic bilevel programs; sensitivity analysis; two-level value functions; generalized differentiation
资金
- Deutscher Akademischer Austausch Dienst (DAAD)
- USA National Science Foundation [DMS-007132]
- Australian Research Council [DP-12092508]
- European Regional Development Fund (FEDER)
- Foundation for Science and Technology, Operational Program for Competitiveness Factors, and Strategic Reference Framework [PTDC/MAT/111809/2009]
- Fundação para a Ciência e a Tecnologia [PTDC/MAT/111809/2009] Funding Source: FCT
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007132] Funding Source: National Science Foundation
This article is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of the corresponding value functions. Several types of lower subdifferential necessary optimality conditions are then derived by using the lower-level value function approach and the Karush-Kuhn-Tucker representation of lower-level optimal solution maps. We also derive upper subdifferential necessary optimality conditions of a new type, which can be essentially stronger than the lower ones in some particular settings. Finally, certain links are established between the obtained necessary optimality conditions for the pessimistic and optimistic versions in bilevel programming.
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