期刊
MATHEMATICAL METHODS OF OPERATIONS RESEARCH
卷 86, 期 2, 页码 255-275出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00186-017-0592-2
关键词
Bilevel programming; Min-max optimization; Nonconvex; Nonsmooth; Newsvendor problem; One-shot decision theory
资金
- JSPS KAKENHI [15K03599]
- Grants-in-Aid for Scientific Research [15K03599] Funding Source: KAKEN
This paper concentrates on solving bilevel programming problems where the lower level programs are max-min optimization problems and the upper level programs have max-max or max-min objective functions. Because these bilevel programming problems include nonconvex and nonsmooth lower level program problems, it is a challenging undone work. Giving some assumptions, we translate these problems into general single level optimization problems or min-max optimization problems. To deal with these equivalent min-max optimization problems, we propose a class of regularization methods which approximate the maximum function by using a family of maximum entropy functions. In addition, we examine the limit situations of the proposed regularization methods and show that any limit points of the global optimal solutions obtained by the approximation methods are the same as the ones of the original problems. Finally, we apply the proposed methods to newsvendor problems and use a numerical example to show their effectiveness.
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