Convergence rates analysis of Interior Bregman Gradient Method for Vector Optimization Problems
Year: 2022
Type: preprint
Abstract: In recent years, by using Bregman distance, the Lipschitz gradient continuity and strong convexity were lifted and replaced by relative smoothness and relative strong convexity. Under the mild assumptions, it was proved that gradient methods with Bregman regularity converge linearly for single-objective optimization problems (SOPs). In this paper, we extend the relative smoothness and relative strong convexity to vector-valued functions and analyze the convergence of an interior Bregman gradient method for vector optimization problems (VOPs). Specifically, the global convergence rates are $\mathcal{O}(\frac{1}{k})$ and $\mathcal{O}(r^{k})(0
Source: arXiv (Cornell University)
Authors: Chen, Jian, Tang, Liping, Yang, Xinmin
Institution: Shanghai University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4283323056