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

被引：0

作者：

S. Dempe

A. B. Zemkoho

机构：

[1] Technische Universität Bergakademie Freiberg,Institut für Numerische Mathematik und Optimierung

来源：

Mathematical Programming | 2013年 / 138卷

关键词：

Bilevel programming; Optimal value function; Constraint qualifications; Optimality conditions; Demand adjustment problem; 90C30; 91A65; 90B06;

D O I：

暂无

中图分类号：

学科分类号：

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.

引用

页码：447 / 473

页数：26

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