SumOfSquares 1.3.1

Python implementation of Sum-of-Squares optimization built on picos

SumOfSquares.py

Documentation	Build Status

Sum of squares optimization built on top of picos. Easy access to pseudoexpectation operators for both formulating problems and extracting solutions via rounding algorithms.

Installation

To install from pypi:

pip install SumOfSquares

Examples

To compute the sum of squares decomposition of a polynomial:

>>> import sympy as sp
>>> x, y = sp.symbols('x y')
>>> p = 2*x**4 + 2*x**3*y - x**2*y**2 + 5*y**4
>>> prob = SOSProblem()
>>> c = prob.add_sos_constraint(p, [x, y])
>>> prob.solve()
>>> c.get_sos_decomp()
Matrix([
[5.0*(-0.306*x**2 + y**2)**2],
[2.057*(0.486*x**2 + x*y)**2],
[                 1.047*x**4]])

More Examples

Citation

If you use this library in your work, please consider citing:

@software{Yuan_SumOfSquares_py,
author = {Yuan, Chenyang},
license = {MIT},
title = {{SumOfSquares.py}},
url = {https://github.com/yuanchenyang/SumOfSquares.py}
}