  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.
