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arXiv · 2412.14007

Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization

Chengzhi Huang·Jian Chen·Liping Tang
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Abstract

This paper proposes a new backtracking strategy based on the FISTA accelerated algorithm for multiobjective optimization problems. The strategy focuses on solving the problem of Lipschitz constant being unknown. It allows estimate parameter updates non-increasingly. Furthermore, the proposed strategy effectively avoids the limitation in convergence proofs arising from the non-negativity of the auxiliary sequence, thus providing a theoretical guarantee for its performance. We demonstrate that, under relatively mild assumptions, the algorithm achieves the convergence rate of $O(1/k2)$.

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Chengzhi Huang, Jian Chen, Liping Tang. 2024-12-18. Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization. https://arxiv.org/abs/2412.14007

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