Linear bilevel problems: Genericity results and an efficient method for computing local minima

Georg J. Still

doi:10.1007/s001860200189

Linear bilevel problems: Genericity results and an efficient method for computing local minima

Georg J. Still

Discrete Mathematics and Mathematical Programming

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11 Citations (Scopus)

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Abstract

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no theoretically efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for efficiently computing local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps.

Original language	English
Pages (from-to)	383-400
Journal	Mathematical methods of operations research
Volume	55
Issue number	3
DOIs	https://doi.org/10.1007/s001860200189
Publication status	Published - 2002

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11 Citations
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Linear bilevel problems: Genericity results and an efficient method for computing local minima
Frederiks, T. J. & Still, G. J., 2000, Enschede: University of Twente. 20 p. (Memorandum; no. 1538)
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AB - The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no theoretically efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for efficiently computing local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps.

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DO - 10.1007/s001860200189

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JO - Mathematical methods of operations research

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Linear bilevel problems: Genericity results and an efficient method for computing local minima

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Linear bilevel problems: Genericity results and an efficient method for computing local minima

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