An accelerated proximal gradient method for multiobjective optimization

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalariz...

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Veröffentlicht in:Computational optimization and applications Jg. 86; H. 2; S. 421 - 455
Hauptverfasser: Tanabe, Hiroki, Fukuda, Ellen H., Yamashita, Nobuo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2023
Springer Nature B.V
Schlagworte:
Algorithms
Convergence
Convex and Discrete Geometry
Iterative methods
Management Science
Mathematics
Mathematics and Statistics
Methods
Multiple objective analysis
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
FISTA
Global rate of convergence
90C25
Multiobjective optimization
Pareto optimality
90C29
First-order method
Proximal gradient method
ISSN:0926-6003, 1573-2894
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Zusammenfassung:This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm, for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ( O ( 1 / k 2 ) ), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments.
Bibliographie:ObjectType-Article-1
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00497-w