Penalty Decomposition Derivative-Free Method

Implementation of the Penalty-Decomposition Derivative-Free (PDDF) method introduced in

Cecere F., Lapucci M., Pucci D. and Sciandrone M. - Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set - arXiv pre-print (2025)

Installation

In order to use PDDF you will need a working conda installation. We suggest the creation of a new conda environment with Python 3.13. The required dependencies numpy and PyNomadBBO can be installed through:

pip install numpy
pip install PyNomadBBO

Another required dependency is PyCUTEst, that can be installed following the installation guide. To run the Lockwood problem make sure to download the source code from Robert Gramacy's Surrogates Website and to compile it. The RUNLOCK_PATH in problems/lockwood.py should be modified accordingly.

Usage

We provide the implementation of PDDF, its parallel version PDDF_P and the implementation of the competitors considered in the paper LS and SALS. Installing PyNomadBBO package it is possible to run also MADS.

In order to run the experiments, execute the following:

python main.py [options]

The following arguments shall be specified:

Short Option	Long Option	Type	Description	Default
-p	--problem_class	str	Class of problems to be executed	None (required)
-a	--algorithm	str	Algorithm to be executed	None (required)
-ld	--logs_dir	str	Path to save the output logs	None (required)
-pause	--pause	float	Pause (in seconds) at each function evaluation	0.
-toll	--toll	float	Termination tolerance	1e-4
-tl	--time_limt	int	Time limit (in seconds)	600

In main.py, the complete list of algorithm parameters can be found and adjusted according to the specific problem considered.

It is possible to run the experiments reported in the paper with:

python main.py -p UNCONSTR -a STD -ld output_dir
python main.py -p BOUNDED -a STD -ld output_dir
python main.py -p LOCKWOOD -a STD -ld output_dir -toll 0.01 -tl 3600

python main.py -p UNCONSTR -a FAST -ld output_dir -pause 0.001 -tl 3600
python main.py -p BOUNDED -a FAST -ld output_dir -pause 0.001 -tl 3600

Credits

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

@misc{cecere2025penaltydecompositionderivativefree,
      title={Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set}, 
      author={Francesco Cecere and Matteo Lapucci and Davide Pucci and Marco Sciandrone},
      year={2025},
      eprint={2503.21631},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/2503.21631}, 
}