Conjugate-gradient with non-negativity constraints

This is a package for minimization of differentiable functions subject to non-negativity constraints on all the variables, i.e.

min f(x)
s.t. x[i] >= 0  i = 1..n

It uses a modified Polak-Ribiere-Polyak method, which is described in the paper "A conjugate gradient type method for the nonnegative constraints optimization problems" (see reference at the end). Implementation is in C with wrappers for Python and R.

This algorithm tends to require more function evaluations than others, but fewer gradient evaluations. It always produces feasible descent directions.

Installation

• Python:

Windows:

git clone https://www.github.com/david-cortes/nonneg_cg.git
cd nonneg_cg
python setup.py install

(Could also be installed from pip depending in NumPy version)

Note: do NOT compile with MINGW in Windows

Linux and Mac

pip install nonnegcg

• R:

devtools::install_github("david-cortes/nonneg_cg")

(Can also be installed with install.packages("nonneg.cg"), but it won't have multithreading support)

• C/C++:

git clone https://www.github.com/david-cortes/nonneg_cg.git
cd nonneg_cg
mkdir build
cd build
cmake ..
make

### for a system-wide install in linux
sudo make install
sudo ldconfig

Usage

• Python: see example notebook here
• R: see example in the documentation (help(minimize.nonneg.cg))
• C/C++: see example file here (- link with -lnonnegcg)

Simple example in Python

import numpy as np
from scipy.optimize import rosen, rosen_der
from nonnegcg import minimize_nncg

x0  = np.array([1.3, 0.7, 0.8, 1.9, 1.2])
res = minimize_nncg(x0, rosen, rosen_der)
res.x

The C function can also be used directly from Rcpp (through R_GetCCallable) and Cython (see .pxd file for the cimport - Python package in addition installs a .h header for usage directly in C by linking to the shared object in nonnegcg.minimize_nncg.__file__)

Documentation

Package has only one function, documentation is available as docstring in Python (help(nonnegcg.minimize_nncg)), as regular documentation in R (help(minimize.nonneg.cg)), and as comment in the header file in C (link here).

References

• Li, C. (2013). A conjugate gradient type method for the nonnegative constraints optimization problems. Journal of Applied Mathematics, 2013.