Trilevel and multilevel optimization using monotone operator theory

Allahkaram Shafiei (), Vyacheslav Kungurtsev () and Jakub Marecek ()
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Allahkaram Shafiei: Czech Technical University
Vyacheslav Kungurtsev: Czech Technical University
Jakub Marecek: Czech Technical University

Mathematical Methods of Operations Research, 2024, vol. 99, issue 1, No 5, 77-114

Abstract: Abstract 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.

Keywords: Variational inequality; Bi-level optimization; Tri-level optimization; Multi-level minimization; Non-expansive mappings (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00186-024-00852-5

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