The bilevel programming problem: reformulations, constraint qualifications and optimality conditions

• 成果类型: Article
• 署名作者: Dempe, S.; Zemkoho, A. B.
• 署名单位: Technical University Freiberg
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0508-5
• 发表日期: 2013
• 页码: 447-473
• 关键词: matrix estimation; optimization; inequalities; STABILITY

摘要

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.