Multicriteria approach to bilevel optimization

被引：60

作者：

Fliege, J. ^{[1
]}

Vicente, L. N.

机构：

[1] Univ Birmingham, Sch Math, Birmingham, W Midlands, England

[2] Univ Erlangen Nurnberg, Inst Appl Math, D-8520 Erlangen, Germany

[3] Univ Coimbra, Dept Matemat, P-3000 Coimbra, Portugal

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2006年 / 131卷 / 02期

关键词：

bilevel optimization; multicriteria optimization;

D O I：

10.1007/s10957-006-9136-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach.

引用

页码：209 / 225

页数：17