Trilevel and Multilevel Optimization using Monotone Operator Theory

We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lo...

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Bibliographic Details
Published inarXiv.org
Main Authors Shafiei, Allahkaram, Kungurtsev, Vyacheslav, Marecek, Jakub
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.10.2023
Subjects
Computational geometry
Computer Science - Artificial Intelligence
Convergence
Convexity
First order algorithms
Fixed points (mathematics)
Mathematics - Optimization and Control
Optimization
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ISSN2331-8422
DOI10.48550/arxiv.2105.09407

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Summary:We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2105.09407