Journal
MATHEMATICAL PROGRAMMING
Volume 138, Issue 1-2, Pages 447-473Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-011-0508-5
Keywords
Bilevel programming; Optimal value function; Constraint qualifications; Optimality conditions; Demand adjustment problem
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Funding
- Deutscher Akademischer Austausch Dienst (DAAD)
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We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially calm without any restrictive assumption. Finally, we consider the bilevel demand adjustment problem in transportation, and show how KKT type optimality conditions can be obtained under the partial calmness, using the differential calculus of Mordukhovich.
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