2024 Volume 67 Issue 1 Pages 1-17
Accelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective optimization problems. However, similarly to the single-objective minimization case, the objective functions values may increase in some iterations, and inexact computations of subproblems can also lead to divergence. Motivated by this, here we propose a variant of the FISTA for multiobjective optimization, that imposes some monotonicity of the objective functions values. In the single-objective case, we retrieve the so-called MFISTA, proposed by Beck and Teboulle. We also prove that our method has global convergence with rate O(1/k2), where k is the number of iterations, and show some numerical advantages in requiring monotonicity.
