An extended Kuhn–Tucker approach for linear bilevel programming

Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principle challenges is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of a...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 162; no. 1; pp. 51 - 63
Main Authors: Shi, Chenggen, Lu, Jie, Zhang, Guangquan
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 04.03.2005
Elsevier
Subjects:
Calculus of variations and optimal control
Decision-making
Exact sciences and technology
Global analysis, analysis on manifolds
Kuhn–Tucker conditions
Linear bilevel programming
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Optimization
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Von Stackelberg game
Kuhn–Tucker conditions
Decision-making
Linear bilevel programming
Optimization
Von Stackelberg game
Numerical analysis
Applied mathematics
Decision making
Optimization method
Linear programming
Kuhn-Tucker conditions
Constrained optimization
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Kuhn–Tucker approach has been applied with remarkable success in linear bilevel programming (BLP). However, it still has some extent unsatisfactory and incomplete. One principle challenges is that it could not well handle a linear BLP problem when the constraint functions at the upper-level are of arbitrary linear form. This paper describes theoretical foundation of Kuhn–Tucker approach and proposes an extended Kuhn–Tucker approach to deal with the problem. The results have demonstrated that the extended Kuhn–Tucker approach can solve a wider class of linear BLP problems can than current capabilities permit.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2003.12.089