How do I tell fmin_cobyla about a matrix constraint Ax-b >= 0? It won't take it as a vector constraint:
cons = lambda x: dot(A,x)-b
thanks.
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2 Answers
Since the constraint must return a scalar value, you could dynamically define the scalar constraints like this:
constraints = []
for i in range(len(A)):
def f(x, i = i):
return np.dot(A[i],x)-b[i]
constraints.append(f)
For example, if we lightly modify the example from the docs,
def objective(x):
return x[0]*x[1]
A = np.array([(1,2),(3,4)])
b = np.array([1,1])
constraints = []
for i in range(len(A)):
def f(x, i = i):
return np.dot(A[i],x)-b[i]
constraints.append(f)
def constr1(x):
return 1 - (x[0]**2 + x[1]**2)
def constr2(x):
return x[1]
x = optimize.fmin_cobyla(objective, [0.0, 0.1], constraints+[constr1, constr2],
rhoend = 1e-7)
print(x)
yields
[-0.6 0.8]
PS. Thanks to @seberg for pointing out an earlier mistake.
Comments
Actually the documentation says Constraint functions;, it simply expects a list of functions each returning only a single value.
So if you want to do it all in one, maybe just modify the plain python code of the fmin_cobyla, you will find there that it defines a wrapping function around your functions, so it is easy... And the python code is really very short anyways, just small wrapper around scipy.optimize._cobyal.minimize.
On a side note, if the function you are optimizing is linear (or quadratic) like your constraints, there are probably much better solvers out there.
