Trilevel and multilevel optimization using monotone operator theory
Mathematical Methods of Operations Research(2024)
摘要
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.
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关键词
Variational inequality,Bi-level optimization,Tri-level optimization,Multi-level minimization,Non-expansive mappings
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