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arXiv · 2206.04412

Monotonicity for Multiobjective Accelerated Proximal Gradient Methods

Yuki Nishimura·Ellen H. Fukuda·Nobuo Yamashita
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Abstract

Accelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective optimization problems. However, similarly to the single-objective minimization case, the objective functions values may increase in some iterations, and inexact computations of subproblems can also lead to divergence. Motivated by this, here we propose a variant of the FISTA for multiobjective optimization, that imposes some monotonicity of the objective functions values. In the single-objective case, we retrieve the so-called MFISTA, proposed by Beck and Teboulle. We also prove that our method has global convergence with rate $O(1/k^2)$, where $k$ is the number of iterations, and show some numerical advantages in requiring monotonicity.

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Yuki Nishimura, Ellen H. Fukuda, Nobuo Yamashita. 2022-06-09. Monotonicity for Multiobjective Accelerated Proximal Gradient Methods. https://arxiv.org/abs/2206.04412

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