Many descent methods for multiobjective optimization problems have been developed in recent years. In 2000, the steepest descent method was proposed for differentiable multiobjective optimization problems. Afterward, the proximal gradient method, which can solve composite problems, was also considered. However, the accelerated versions are not sufficiently studied. In this paper, we propose a multiobjective accelerated proximal gradient algorithm, in which we solve subproblems with terms that only appear in the multiobjective case. We also show the proposed method's global convergence rate ($O(1/k^2)$) under reasonable assumptions, using a merit function to measure the complexity. Moreover, we present an efficient way to solve the subproblem via its dual, and we confirm the validity of the proposed method through preliminary numerical experiments.

翻译：近些年来,为多重目标优化问题制定了许多从属方法。2000年,针对不同的多目标优化问题提出了最陡峭的从属方法。随后,还审议了能够解决复杂问题的近似梯度方法。然而,对加速版的研究不够充分。在本文件中,我们建议采用多客观加速近似梯度算法,用只出现在多目标案例中的术语来解决次级问题。我们还在合理假设下展示了拟议方法的全球趋同率(O(1/k ⁇ 2)$),使用量才函数来衡量复杂性。此外,我们提出了通过双重方法有效解决次级问题的方法,并通过初步数字实验确认了拟议方法的有效性。