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

• URL: http://arxiv.org/abs/2402.06224v1
• Date: Fri, 9 Feb 2024 07:20:14 GMT
• Title: Adaptive multi-gradient methods for quasiconvex vector optimization and applications to multi-task learning
• Authors: Nguyen Anh Minh and Le Dung Muu and Tran Ngoc Thang
• Abstract summary: We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonobjective multi-size programming problems. We prove an unbounded convergence set on modest assumptions. We apply the proposed technique to some multi-task experiments to show efficacy for largescale challenges.
• Score: 1.03590082373586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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