This code repository provides a solver for the proximal gradient method (ISTA) and its acceleration (FISTA) for both single and multi-objective optimization problems, including the experimental code for the Paper1 and Paper2.

An accelerated proximal gradient method for multiobjective optimization
Hiroki Tanabe, Ellen H. Fukuda, and Nobuo Yamashita

A globally convergent fast iterative shrinkage-thresholding algorithm with a new momentum factor for single and multi-objective convex optimization
Hiroki Tanabe, Ellen H. Fukuda, and Nobuo Yamashita

The solver can deal with the unconstrained problem written by $$\min_{x \in \mathbf{R}^n} \quad F(x) \coloneqq f(x) + g(x),$$ where $f$ and $g$ are scalar or vector valued function, $f$ is continuously differentiable, $g$ is closed, proper and convex. Note that FISTA also requires $f$ to be convex.

• Python 3.7 or later

pip install zfista

from zfista import minimize_proximal_gradient
help(minimize_proximal_gradient)

You can run some examples on jupyter notebooks.

jupyter notebook

To set up development environment, run

python -m venv venv
source venv/bin/activate
python -m pip install --upgrade pip
pip install -r requirements.txt

You can run all tests by

python -m unittest discover