Gauss–Newton-type methods for bilevel optimization

Jörg Fliege (), Andrey Tin () and Alain Zemkoho ()
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Jörg Fliege: Management Sciences and Information Systems (CORMSIS)
Andrey Tin: Management Sciences and Information Systems (CORMSIS)
Alain Zemkoho: Management Sciences and Information Systems (CORMSIS)

Computational Optimization and Applications, 2021, vol. 78, issue 3, No 5, 793-824

Abstract: Abstract This article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First, under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss–Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss–Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

Keywords: Bilevel optimization; Value function reformulation; Partial exact penalization; Gauss-Newton method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-020-00254-3

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