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arXiv · 2402.06224

Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning

Nguyen Anh Minh·Le Dung Muu·Tran Ngoc Thang
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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.

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Nguyen Anh Minh, Le Dung Muu, Tran Ngoc Thang. 2024-02-09. Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning. https://arxiv.org/abs/2402.06224

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