使用矩阵约束进行scipy.optimize

Question

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.

Answer 1

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.

Answer 2

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.