论文标题
多目标优化的加速近端梯度方法
An accelerated proximal gradient method for multiobjective optimization
论文作者
论文摘要
本文提出了一种加速近端梯度方法，用于多目标优化，其中每个目标函数是连续区分，凸功能和封闭，正确的凸功能的总和。已经广泛研究了不标量化的多物镜问题的一阶方法，但提供了加速方法，并提供了准确的收敛速度证明仍然是一个开放的问题。我们提出的方法是对加速近端梯度方法的多物镜概括，也称为快速迭代式收缩率阈值算法（FISTA），以进行标量优化。成功扩展的关键是用多目标案例独有的术语解决一个子问题。这种方法使我们能够使用优点函数来测量拟议方法的全局收敛速率（$ o（1 / k^2）$）。此外，我们提出了一种通过其双重表示来解决子问题的有效方法，并通过一些数值实验确认了该方法的有效性。
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ($O(1 / k^2)$), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments.
