PyCPX Introduction¶

PyCPX is a python wrapper for the CPlex optimization suite that focuses on ease of use and seamless integration with numpy. It allows one to naturally specify linear and quadratic problems over real, boolean, and integer variables. PyCPX allows one to naturally express such programs using numpy and natural python constructs.

It requires IBM’s ILog Concert Technology Suite, part of the CPlex Optimization Suite, which is available for free to eligible academic researchers under IBM’s Academic Initiative program.

Version 0.02 fixes several small bugs and gives vast speed improvements for model creation in many models.

PyCPX Distinctives¶

• Seamless integration with Numpy arrays.
• Easy and natural syntax using CPlex Concert technology.
• Written in cython/C++ for speed.
• The API is well documented and covered by unit tests.

Short Example¶

A brief example to wet the appetite:

```>>> import numpy as np
>>> from PyCPX import CPlexModel
>>>
>>> A = np.array([[1,0,0], [1,1,0], [1,1,1]])
>>> b = np.array([1,2,3])
>>>
>>> m = CPlexModel()
>>>
>>> x = m.new(3)
>>> t = m.new()
>>>
>>> m.constrain( abs((A*x - b)) <= t)
>>> m.minimize(t)
0.0
>>> m[x]
array([ 1.,  1.,  1.])
```

A more detailed example:

```>>> from PyCPX import CPlexModel
>>> from numpy import array, arange
>>>
>>> A = 2*arange(1,10).reshape( (3, 3) )
>>> m = CPlexModel()
>>>
>>> X = m.new( (3, 3), vtype = int)
>>> u = m.new( 3, vtype = int)
>>> s = m.new(vtype = int)
>>>
>>> m.constrain(s <= A.T * X <= 10*s)
>>> m.constrain(1 <= X.sum(axis = 1) <= u)
>>>
>>> m.minimize(u.sum())
3.0
>>> m[X]
matrix([[-2.,  3.,  0.],
[ 0.,  0.,  1.],
[ 1.,  0.,  0.]])
>>> m[u]
array([ 1.,  1.,  1.])
>>> m[s]
2.0
>>> m[X[0,0]]
-2.0
```