An accelerated proximal gradient method for multiobjective optimization

Hiroki Tanabe (), Ellen H. Fukuda () and Nobuo Yamashita ()
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Hiroki Tanabe: Yahoo Japan Corporation
Ellen H. Fukuda: Kyoto University
Nobuo Yamashita: Kyoto University

Computational Optimization and Applications, 2023, vol. 86, issue 2, No 1, 455 pages

Abstract: Abstract 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 ( $$O(1 / k^2)$$ 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.

Keywords: Multiobjective optimization; Proximal gradient method; Pareto optimality; Global rate of convergence; First-order method; FISTA; 90C25; 90C29 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-023-00497-w

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