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- Title
Trilevel and multilevel optimization using monotone operator theory.
- Authors
Shafiei, Allahkaram; Kungurtsev, Vyacheslav; Marecek, Jakub
- 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.
- Subjects
MONOTONE operators; OPERATOR theory; FIXED point theory; NONEXPANSIVE mappings; CONVEX functions
- Publication
Mathematical Methods of Operations Research, 2024, Vol 99, Issue 1/2, p77
- ISSN
1432-2994
- Publication type
Article
- DOI
10.1007/s00186-024-00852-5