The convergence rate of the accelerated proximal gradient algorithm for Multiobjective Optimization is faster than $O(1/k^2)$

Jie Zhang; Xinmin Yang

The convergence rate of the accelerated proximal gradient algorithm for Multiobjective Optimization is faster than $O(1/k^2)$

Optimization and Control 2023-12-13 v1

Authors: Jie Zhang , Xinmin Yang

Abstract

In this paper, we propose a fast proximal gradient algorithm for multiobjective optimization, it is proved that the convergence rate of the accelerated algorithm for multiobjective optimization developed by Tanabe et al. can be improved from $O(1/k^2)$ to $o(1/k^2)$ by introducing different extrapolation term $\frac{k-1}{k+\alpha-1}$ with $\alpha>3$ . Further, we establish the inexact version of the proposed algorithm when the error term is additive, which owns the same convergence rate. At last, the efficiency of the proposed algorithm is verified on some numerical experiments.

Keywords

accelerated gradient methods stochastic optimization optimization

Cite

@article{arxiv.2312.06913,
  title  = {The convergence rate of the accelerated proximal gradient algorithm for Multiobjective Optimization is faster than $O(1/k^2)$},
  author = {Jie Zhang and Xinmin Yang},
  journal= {arXiv preprint arXiv:2312.06913},
  year   = {2023}
}

Related papers

View all related →