Bilevel optimization: on the structure of the feasible set
type: Item
instance of: scholarly article
title: Bilevel optimization: on the structure of the feasible set
zbMATH Open document ID: 1286.90150
author: Hubertus T. Jongen
author: Vladimir Shikhman
published in: Mathematical Programming. Series A. Series B
publication date: 2012-12-19T00:00:00Z
review text: The authors consider a class of bilevel optimization problems treated also as a leader-follower problem from the optimistic point of view. The coupling constraints are presented in both problems. The authors investigate properties of the leader feasible set in the case where his/her variable dimension is equal to one. They show that it is the union of \(C^2\) curves with boundary points and kinks, which can be parametrized via this variable. Some examples describing the same problems in higher dimensions are also discussed.
reviewed by: Igor V. Konnov
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 6116935
zbMATH Keywords: bilevel programming
zbMATH Keywords: coupling constraints
zbMATH Keywords: parametric optimization
zbMATH Keywords: structure of the feasible set
MaRDI profile type: Publication
full work available at URL: s10107-012-0551-x
OpenAlex ID: W2037904604
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DOI: 10.1007/S10107-012-0551-X
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description: scientific article; zbMATH DE number 6116935