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Comput Optim Appl (2009) 43: 307328 DOI 10.1007/s10589-007-9147-4

Summary: Comput Optim Appl (2009) 43: 307­328
DOI 10.1007/s10589-007-9147-4
An inexact-restoration method for nonlinear bilevel
programming problems
R. Andreani · S.L.C. Castro · J.L. Chela ·
A. Friedlander · S.A. Santos
Received: 11 December 2006 / Revised: 19 October 2007 / Published online: 20 November 2007
© Springer Science+Business Media, LLC 2007
Abstract We present a new algorithm for solving bilevel programming problems
without reformulating them as single-level nonlinear programming problems. This
strategy allows one to take profit of the structure of the lower level optimization
problems without using non-differentiable methods. The algorithm is based on the
inexact-restoration technique. Under some assumptions on the problem we prove
global convergence to feasible points that satisfy the approximate gradient projection
(AGP) optimality condition. Computational experiments are presented that encourage
the use of this method for general bilevel problems.
Keywords Bilevel programming · Inexact-restoration · Optimization
This work was supported by PRONEX-Optimization (PRONEX--CNPq/FAPERJ
E-26/171.164/2003--APQ1), FAPESP (Grants 06/53768-0 and 05-56773-1) and CNPq.
R. Andreani · A. Friedlander ( ) · S.A. Santos


Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas


Collections: Mathematics