Journal of Global Optimization

, Volume 38, Issue 4, pp 527–554 | Cite as

A novel approach to Bilevel nonlinear programming

Article

Abstract

Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the monotonic approach is extended to the General Bilevel Programming GBP Problem. It is shown that (GBP) can be transformed into a monotonic optimization problem which can then be solved by “polyblock” approximation or, more efficiently, by a branch-reduce-and-bound method using monotonicity cuts. The method is particularly suitable for Bilevel Convex Programming and Bilevel Linear Programming.

Keywords

Bilevel nonlinear programming Bilevel convex programming Bilevel linear programming Leader and follower game Monotonic optimization Polyblock approximation Branch-reduce-and-bound method Monotonicity cuts 

AMS subject classification

90C26 65K05 90C20 90C30 90C56 78M50 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Technical University of CreteCreteGreece

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