Optimality conditions for the bilevel programming problem
作者:
Jonathan F. Bard,
期刊:
Naval Research Logistics Quarterly
(WILEY Available online 1984)
卷期:
Volume 31,
issue 1
页码: 13-26
ISSN:0028-1441
年代: 1984
DOI:10.1002/nav.3800310104
出版商: Wiley Subscription Services, Inc., A Wiley Company
数据来源: WILEY
摘要:
AbstractThe bilevel programming problem (BLPP) is a sequence of two optimization problems where the constraint region of the first is determined implicitly by the solution to the second. In this article it is first shown that the linear BLPP is equivalent to maximizing a linear function over a feasible region comprised of connected faces and edges of the original polyhedral constraint set. The solution is shown to occur at a vertex of that set. Next, under assumptions of differentiability, first‐order necessary optimality conditions are developed for the more general BLPP, and a potentially equivalent mathematical program is formulated. Finally, the relationship between the solution to this problem and Pareto optimality is discussed and a number of examples give
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