PDFO: Powell's Derivative-Free Optimization solvers

Introduction | Python | MATLAB | Citing PDFO | Acknowledgments

Dedicated to the late Professor M. J. D. Powell FRS (1936–2015).

Introduction

PDFO (Powell's Derivative-Free Optimization solvers) is a cross-platform package providing interfaces for using the late Professor M. J. D. Powell's derivative-free optimization solvers, including UOBYQA, NEWUOA, BOBYQA, LINCOA, and COBYLA. See the PDFO homepage and the PDFO paper for more information.

This package makes use of a modified version of Powell's Fortran code. See the folder original under fsrc for Powell's original code.

Python version of PDFO

Installation

Recommended installation

To use the Python version of PDFO on Linux, Mac, or Windows, you need Python (version 3.8 or above).

It is highly recommended to install PDFO via PyPI.

Install pip in your system if you Python version does not include it. Then execute

pip install pdfo

in a command shell (e.g., the terminal for Linux and macOS, or the Command Shell for Windows). If your pip launcher is not pip, adapt the command accordingly (it may be pip3 for example). If this command runs successfully, PDFO is installed. You may verify the installation by

python -m unittest pdfo.testpdfo

Once again, if your Python launcher is not python, adapt the command accordingly (it may be python3 for example). If you are an Anaconda user, PDFO is also available through the conda installer ( https://anaconda.org/conda-forge/pdfo ). However, it is not managed by us.

Alternative installation (using source distribution)

Alternatively, although deeply discouraged, PDFO can be installed from the source code. It requires you to install additional Python headers, a Fortran compiler (e.g., gfortran), and F2PY (provided by NumPy). Download and decompress the source code package, or clone it from GitHub or Gitee. You will obtain a folder containing pyproject.toml; in a command shell, change your directory to this folder; then install PDFO by executing

pip install .

Usage

PDFO provides a Python function pdfo, which can solve general constrained or unconstrained optimization problems without using derivatives.

The pdfo function can automatically identify the type of your problem and then call one of Powell’s solvers, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. The user can also specify the solver by setting the method field of the options passed to pdfo.

The pdfo function is designed to be compatible with the scipy.optimize.minimize function of SciPy. You can call pdfo in exactly the same way as calling scipy.optimize.minimize except that pdfo does not accept derivative arguments.

For the detailed syntax of pdfo, use the standard help command of Python:

from pdfo import pdfo
help(pdfo)

Uninstall

PDFO can be uninstalled by executing the following command in a command shell:

python3 -m pip uninstall pdfo

MATLAB version of PDFO

Prerequisites

PDFO supports MATLAB R2014a and later releases. To use PDFO, you need first set up the MEX of your MATLAB so that it can compile Fortran. The setup of MEX is a pure MATLAB usage problem and it has nothing to do with PDFO.

To see whether your MEX is ready, run the following code in MATLAB:

mex('-setup', '-v', 'fortran'); mex('-v', fullfile(matlabroot, 'extern', 'examples', 'refbook', 'timestwo.F'));

If this completes successfully, then your MEX is ready. Otherwise, it is not, and you may try the setup_mex package at

https://github.com/equipez/setup_mex

It will help you to set MEX up on Windows or macOS (the setup of MEX is trivial on Linux). In case setup_mex does not work, you need to consult a local MATLAB expert or the technical support of MathWorks about "how to set up MEX", which is not part of PDFO.

Installation

Download and decompress the source code package, or clone it from GitHub or Gitee. You will obtain a folder containing setup.m. Place this folder at the location where you want PDFO to be installed. In MATLAB, change the directory to this folder, and execute the following command:

setup

If this command runs successfully, PDFO is installed. You may execute the following command in MATLAB to verify the installation:

testpdfo

Usage

PDFO provides a MATLAB function pdfo, which can solve general constrained or unconstrained optimization problems without using derivatives.

The pdfo function can automatically identify the type of your problem and then call one of Powell’s solvers, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. The user can also specify the solver by setting the solver field of the options passed to pdfo.

The pdfo function is designed to be compatible with the fmincon function available in the Optimization Toolbox of MATLAB. You can call pdfo in the same way as calling fmincon. In addition, pdfo can be called in some flexible ways that are not supported by fmincon.

For detailed syntax of pdfo, use the standard help command of MATLAB:

help pdfo

Uninstall

PDFO can be uninstalled using the setup.m script by executing the following command in MATLAB:

setup uninstall

Citing PDFO

If you use PDFO, please cite the following paper. Note that PDFO contains improvements and bug fixes that do not exist in Powell's original code. See Subsections 4.3--4.5 of the paper for details.

[1] T. M. Ragonneau and Z. Zhang, PDFO: a cross-platform package for Powell's derivative-free optimization solvers, arXiv:2302.13246, 2023.

@misc{Ragonneau_Zhang_2023,
    title        = {{PDFO}: a cross-platform package for {Powell}'s derivative-free optimization solvers},
    author       = {Ragonneau, T. M. and Zhang, Z.},
    howpublished = {arXiv:2302.13246},
    year         = 2023
}

In addition, Powell’s methods can be cited as follows.

[2] M. J. D. Powell. A direct search optimization method that models the objective and constraint functions by linear interpolation. In S. Gomez and J. P. Hennart, editors, Advances in Optimization and Numerical Analysis, pages 51–67, Dordrecht, NL, 1994. Springer.

[3] M. J. D. Powell. UOBYQA: unconstrained optimization by quadratic approximation. Math. Program., 92:555–582, 2002.

[4] M. J. D. Powell. The NEWUOA software for unconstrained optimization without derivatives. In G. Di Pillo and M. Roma, editors, Large-Scale Nonlinear Optimization, volume 83 of Nonconvex Optimization and Its Applications, pages 255–297, Boston, MA, USA, 2006. Springer.

[5] M. J. D. Powell. The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report DAMTP 2009/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2009.

Remark: LINCOA seeks the least value of a nonlinear function subject to linear inequality constraints without using derivatives of the objective function. Powell did not publish a paper to introduce the algorithm.

Acknowledgments

PDFO is dedicated to the memory of the late Professor Powell with gratitude for his inspiration and for the treasures he left to us.

We are grateful to Professor Ya-xiang Yuan for his everlasting encouragement and support.

The development of PDFO is a long-term project, which would not be sustainable without the continued funds from the Hong Kong Research Grants Council (ref. PolyU 253012/17P, PolyU 153054/20P, and PolyU 153066/21P), the Hong Kong Ph.D. Fellowship Scheme (ref. PF18-24698), and the Hong Kong Polytechnic University (PolyU), in particular the Department of Applied Mathematics (AMA).