Solving linear fractional bilevel programs.
type: Item
instance of: scholarly article
title: Solving linear fractional bilevel programs.
zbMATH Open document ID: 1036.90068
author: Herminia I. Calvete
author: Carmen Galé
published in: Operations Research Letters
publication date: 2004-01-05T00:00:00Z
review text: The authors give a geometrical characterization of the optimal solution to the linear fractional bilevel programming (LFBP) problem in terms of what is called a boundary feasible extreme point. It is assumed that the second level optimal solution sets are singletons. The results extend the characterization proved by \textit{Y. H. Liu} and \textit{S. M. Hart} [Eur. J. Oper. Res. 73, 164--166 (1994; Zbl 0806.90084)] for the linear bilevel programming problem. Based on this property the authors show that the \(K\)th-best algorithm can be used to solve the LFBP problem. This algorithm was first proposed by \textit{W. F. Bialas} and \textit{M. H. Karwan} [Manage. Sci. 30, 1004--1020 (1984; Zbl 0559.90053)] for solving the linear bilevel programming problem. An example is included to illustrate the application of the algorithm. Finally, the last section includes some remarks on quasiconcave bilevel problems for which the characterization of the optimal solution is still valid and the \(K\)th-best algorithm can be applied to solve them.
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C08
zbMATH DE Number: 2021244
zbMATH Keywords: linear bilevel programming
zbMATH Keywords: linear fractional bilevel programming
zbMATH Keywords: fractional
zbMATH Keywords: quasiconcave bilevel problems
zbMATH Keywords: Kth-best algorithm
reviewed by: Francisco Guerra Vazquez
MaRDI profile type: Publication
full work available at URL: j.orl.2003.07.003
OpenAlex ID: W2063685085
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DOI: 10.1016/J.ORL.2003.07.003
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description: scientific article; zbMATH DE number 2021244