Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 31, Issue 4, Pages 811-824Publisher
INFORMS
DOI: 10.1287/moor.1060.0219
Keywords
necessary optimality conditions; constraint qualifications; nonsmooth analysis; value function; bilevel programming problems
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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.
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