Optimality conditions for bilevel programming problems
Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the fea...
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| Vydané v: | Optimization Ročník 55; číslo 5-6; s. 505 - 524 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Philadelphia
Taylor & Francis Group
01.10.2006
Taylor & Francis LLC |
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| ISSN: | 0233-1934, 1029-4945 |
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| Abstract | Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the feasible set as necessary optimality condition we need efficient ways to describe this tangent cone. We describe possibilities for this in three different special cases. We conclude this article with the second approach applying Mordukhovich's coderivative to an appropriately reformulated bilevel programming problem. |
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| AbstractList | Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the feasible set as necessary optimality condition we need efficient ways to describe this tangent cone. We describe possibilities for this in three different special cases. We conclude this article with the second approach applying Mordukhovich's coderivative to an appropriately reformulated bilevel programming problem. Focus in the article is on necessary optimality conditions for bilevel programming problems. We first identify approaches that seem to be promising. Then, two such approaches are investigated. Using the nonexistence of a descent direction for the objective function within the tangent cone to the feasible set as necessary optimality condition we need efficient ways to describe this tangent cone. We describe possibilities for this in three different special cases. We conclude this article with the second approach applying Mordukhovich's coderivative to an appropriately reformulated bilevel programming problem. [PUBLICATION ABSTRACT] |
| Author | Dempe, S. Lohse, S. Dutta, J. |
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| References | Dempe S (CIT0006) 1996; 6 CIT0012 CIT0011 Dempe S (CIT0004) 2002 Outrata J (CIT0018) 2000; 30 Dutta J (CIT0009) 2005 Luo Z-Q (CIT0013) 1996 Bank B (CIT0002) 1982 CIT0014 CIT0015 Mordukhovich BS (CIT0016) 2005 CIT0019 CIT0021 CIT0020 CIT0023 Bard JF (CIT0003) 1998 CIT0022 Outrata J (CIT0017) 1998 Jahn J (CIT0010) 2004 Babahadda H (CIT0001) 2005 CIT0025 CIT0024 CIT0005 CIT0026 CIT0007 CIT0008 |
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| Title | Optimality conditions for bilevel programming problems |
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