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Simplicial homology global optimisation

## Project description

Repository: https://github.com/Stefan-Endres/shgo

## Description

Finds the global minimum of a function using simplicial homology global optimisation (shgo_). Appropriate for solving general purpose NLP and blackbox optimisation problems to global optimality (low dimensional problems). The general form of an optimisation problem is given by:

::

minimize f(x) subject to

g_i(x) >= 0,  i = 1,...,m
h_j(x)  = 0,  j = 1,...,p


where x is a vector of one or more variables. f(x) is the objective function R^n -> R, g_i(x) are the inequality constraints. h_j(x) are the equality constrains.

## Installation

Stable:

.. code::

$pip install shgo  Latest: .. code:: $ git clone https://github.com/Stefan-Endres/shgo
$cd shgo$ python setup.py install
\$ python setup.py test


## Documentation

The project website https://stefan-endres.github.io/shgo/ contains more detailed examples, notes and performance profiles.

## Quick example

Consider the problem of minimizing the Rosenbrock function. This function is implemented in rosen in scipy.optimize

.. code:: python

>>> from scipy.optimize import rosen
>>> from shgo import shgo
>>> bounds = [(0,2), (0, 2), (0, 2), (0, 2), (0, 2)]
>>> result = shgo(rosen, bounds)
>>> result.x, result.fun
(array([ 1.,  1.,  1.,  1.,  1.]), 2.9203923741900809e-18)


Note that bounds determine the dimensionality of the objective function and is therefore a required input, however you can specify empty bounds using None or objects like numpy.inf which will be converted to large float numbers.

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