Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization

2024/12/18 by Cheng-Zhi Anna Huang, Jian Chen, Huang, Chengzhi +3
Computer Science · #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Neural Networks and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2412.14007

openalex publication_date 2024/12/18 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28

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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