Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
Abstract
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general approach under modest assumptions. More specifically, the convexity criterion might not be satisfied by the objective function. Unlike descent line-search algorithms, it does not require an initial step-size to be determined by a previously determined Lipschitz constant. The process's primary characteristic is its gradual step-size reduction up until a predetermined condition is met. It can be specifically applied to offer an innovative multi-gradient projection method for unbounded constrained optimization issues. Preliminary findings from a few computational examples confirm the accuracy of the strategy. We apply the proposed technique to some multi-task learning experiments to show its efficacy for large-scale challenges.
Cite
@article{arxiv.2402.06224,
title = {Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning},
author = {Nguyen Anh Minh and Le Dung Muu and Tran Ngoc Thang},
journal= {arXiv preprint arXiv:2402.06224},
year = {2024}
}