# Monotonicity for Multiobjective Accelerated Proximal Gradient Methods

arXiv: https://arxiv.org/abs/2206.04412 · HTML: https://mlsanity.com/paper/2206.04412/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Complexity Bounds for Smooth Multiobjective Optimization](https://mlsanity.com/paper/2509.13550/) (2025)

## Abstract (arXiv)

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.