Constraint qualifications and KKT conditions for bilevel programming problems

• 成果类型: Article
• 署名作者: Ye, Jane J.
• 署名单位: University of Victoria
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0219
• 发表日期: 2006
• 页码: 811-824
• 关键词: mathematical programs; optimization problems; stationarity; optimality

摘要

In this paper we consider the bilevel programming problem (BLPP), which is a sequence of two optimization problems where the constraint region of the upper-level problem is determined implicitly by the solution set to the lower-level problem. We extend well-known constraint qualifications for nonlinear programming problems such as the Abadie constraint qualification, the Kuhn-Tucker constraint qualification, the Zangwill constraint qualification, the Arrow-Hurwicz-Uzawa constraint qualification, and the weak reverse convex constraint qualification to BLPPs and derive a Karash-Kuhn-Tucker (KKT)-type necessary optimality condition under these constraint qualifications without assuming the lower-level problem satisfying the Mangasarian Fromovitz constraint qualification. Relationships among various constraint qualifications are also given.