Gauss–Newton-type methods for bilevel optimization
| Autor: | Jörg Fliege, Andrey Tin, Alain B. Zemkoho |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematical optimization
Computer Science::Computer Science and Game Theory 021103 operations research Control and Optimization Applied Mathematics Gauss 0211 other engineering and technologies Mathematics::Optimization and Control 010103 numerical & computational mathematics 02 engineering and technology Type (model theory) 01 natural sciences Bilevel optimization Continuous variable Computational Mathematics Bellman equation Complementarity (molecular biology) Convergence (routing) 0101 mathematics Smoothing Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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