Gradient Method with Momentum (GMM)

Implementation of a globally convergent gradient method with momentum presented in

M. Lapucci, G. Liuzzi, S. Lucidi, D.Pucci and M. Sciandrone - A Globally Convergent Gradient Method with Momentum - arXiv:2403.17613 [math.OC]

Installation

A working Anaconda installation is required. We suggest the creation of a new conda environment with Python 3.11. All the required packages can be installed with:

pip install -r requirements.txt

To execute CUTEst experiments, make sure that the problems are locally installed. We report the .SIF problem definitions used in the experiment; these correspond to the default .SIF files downloaded when installing CUTEst.

Usage

The experiments can be executed using:

python main_gmm.py [options]

The following arguments shall be specified:

Short Option	Long Option	Type	Description	Default
-p	--problem	str	Problem Name	None (required)
-g_tol	--grad_tol	float	Termination condition on the gradient $\ell_\infty$-norm	1e-6
-m_iter	--max_iter	int	Termination condition on the number of iterations	100000

Acknowledgements

The results of the experiments reported in Section 7 are avaialble in the Results folder. The performance profiles shown in the paper are also avialable in the same folder. We also report the results of cg_descent executed from SuiteOPT for reference.

In case you employed our code for research purposes, please cite:

@misc{lapucci2024globallyconvergentgradientmethod,
      title={A Globally Convergent Gradient Method with Momentum}, 
      author={Matteo Lapucci and Giampaolo Liuzzi and Stefano Lucidi and Davide Pucci and Marco Sciandrone},
      year={2024},
      eprint={2403.17613},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2403.17613}, 
}