Why when using Mystic in Python to optimise a non linear constrained optimisation do I receive a 'cannot simply inequalities' error?

Question

I am trying to optimise the problem below using Mystic. I am currently receiving an error that I don't understand and was hoping someone more familiar with the library could help.

def objective(x):
    x0,x1,x2,x3,x4,x5,x6,x7,x8 = x
    return x0**2 + x4**2 + x8**2
equations = '''
x0 + x1 + x2 - x3 - x6 - 20 == 0.0
x4 + x3 + x5 - x1 - x7 - 150 == 0.0
x8 + x6 + x7 - x2 - x5 + 100 == 0.0
x6 == 0
x7 == 0
x0 >= 10
x4 >= 60
'''
from mystic.symbolic import generate_conditions, generate_penalty
pf = generate_penalty(generate_conditions(equations), k=1e4)
from mystic.symbolic import generate_constraint, generate_solvers, solve
cf = generate_constraint(generate_solvers(solve(equations))

When calculating cf i receive an 'NotImplementedError:cannot simplify inequalities' and wanted to know why this could be? If anyone knows how i would extend this such that i can create the constraints through a function or in a different manner I would also be keen to know. Cheers

Answer 1

I'm the mystic author. You should always first try just using solve(equations) and see what happens. It can fail to symbolically solve the equations due to the inequalities. If so, then try to do simplify(equalities) instead. That symbolically simplifies equations so there's only one variable on the LHS for each line. The inequality solver usually can then work in that case. If that fails, you can rewrite the equations so there's only one variable on the LHS.

>>> def objective(x):
...     x0,x1,x2,x3,x4,x5,x6,x7,x8 = x
...     return x0**2 + x4**2 + x8**2
... 
>>> import mystic
>>> equations = '''
... x0 + x1 + x2 - x3 - x6 - 20 == 0.0
... x4 + x3 + x5 - x1 - x7 - 150 == 0.0
... x8 + x6 + x7 - x2 - x5 + 100 == 0.0
... x6 == 0
... x7 == 0
... x0 >= 10
... x4 >= 60
... '''
>>> eqns = mystic.symbolic.simplify(equations)
>>> print(eqns)
x0 == -x1 - x2 + x3 + x6 + 20
x8 == x2 + x5 - x6 - x7 - 100
x4 >= 60
x7 == 0
x6 == 0
x0 >= 10
x4 == x1 - x3 - x5 + x7 + 150
>>> from mystic.symbolic import generate_constraint, generate_solvers 
>>> cf = generate_constraint(generate_solvers(eqns))
>>> cf([0,1,2,3,4,5,6,7,8])
[26, 1, 2, 3, 143, 5, 0, 0, -106]
>>>