Optimality results for a specific bilevel optimization problem

被引:1
|
作者
Dempe, S. [1 ]
Gadhi, N. [2 ]
机构
[1] Tech Univ Bergakad Freiberg, D-09596 Freiberg, Germany
[2] Sidi Mohamed Ben Abdellah Univ, Dept Math, Fes, Morocco
关键词
bilevel optimization; extremal principle; Frechet normal cone; optimality conditions;
D O I
10.1080/02331931003596725
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We develop necessary optimality conditions using techniques from variational analysis for a bilevel optimization problem without assuming the lower-level problem satisfying neither the Mangasarian Fromovitz constraint qualification nor the partial calmness condition [D. L. Ye and D. L. Zhu, Optimality conditions for bilevel programming problems, Optimization 33 (1995), pp. 9-27; J.J. Ye and J.J. Zhu, A note on optimality conditions for bilevel programming problems, Optimization 39 (1997), pp. 361-366]. Reducing the problem into a one-level nonlinear and nonsmooth programme, we use the approximate extremal principle [B. S. Mordukhovich, Variational Analysis and Generalized Differentiation: I. Basic Theory, Grundlehren Series, Fundamental Principles of Mathematical Sciences, Vol. 330, Springer, Berlin, 2006; B. S. Mordukhovich, Variational Analysis and Generalized Differentiation: II. Applications, Grundlehren Series, Fundamental Principles of Mathematical Sciences, Vol. 331, Springer, Berlin, 2006] to get fuzzy and exact optimality conditions.
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页码:813 / 822
页数:10
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