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- Title
Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming.
- Authors
Dempe, Stephan; Pilecka, Maria
- Abstract
In this paper we adapt the main results from Amahroq and Gadhi (J Glob Optim 21:435-443, ) for a general set-valued optimization problem to an optimistic bilevel programming problem as an optimization problem with implicitly given set-valued constraint. Since this constraint is assumed to be upper but not lower semicontinuous in the sense of Berge, we need to deal with a lower semicontinuous distance function to this mapping. In order to approximate the gradient of the distance function, we introduce a new concept for a directional convexificator. Some calculus rules for this new tool are adapted and several properties are characterized. The main result presents optimality conditions for an optimistic bilevel programming problem using a convexificator constructed with the aid of the directional convexificator.
- Subjects
BILEVEL programming; MATHEMATICAL optimization; CONSTRAINT algorithms; CONSTRAINT programming; CALCULUS software
- Publication
Journal of Global Optimization, 2015, Vol 61, Issue 4, p769
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-014-0200-4