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MONOTONICITY FOR MULTIOBJECTIVE ACCELERATED PROXIMAL GRADIENT METHODS

Yuki Nishimura et al.

Journal of the Operations Research Society of Japan2024https://doi.org/10.15807/jorsj.67.1article
ABDC B
Weight
0.36

What the paper says

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/k2), where k is the number of iterations, and show some numerical advantages in requiring monotonicity.

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https://doi.org/https://doi.org/10.15807/jorsj.67.1

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@article{yuki2024,
  title        = {{MONOTONICITY FOR MULTIOBJECTIVE ACCELERATED PROXIMAL GRADIENT METHODS}},
  author       = {Yuki Nishimura et al.},
  journal      = {Journal of the Operations Research Society of Japan},
  year         = {2024},
  doi          = {https://doi.org/https://doi.org/10.15807/jorsj.67.1},
}

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Evidence weight

0.36

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.13 × 0.4 = 0.05
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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