How to minimize function like this

Question

Function:

def Phi(u, X):
    return -(1+u[0]*X[0]+u[1]*X[1]+u[2]*X[2]+u[3]*X[3])

And I know that X[0]...X[3] is in [-0.08,0.08] and u[0],u[1],u[2],u[3] >= 0 and u[0]+u[1]+u[2]+u[3] = 1, also I know gradient of my functions. Then I defined constraint:

def constraint1(u):
    return u[0]+u[1]+u[2]+u[3]-1.0
def constraint2(u):
    return u[0]-1.0
def constraint3(u):
    return u[1]-1.0
def constraint4(u):
    return u[2]-1.0
def constraint5(u):
    return u[3]-1.0

And bounds

bnds = Bounds ([-0.08, -0.08, -0.08], [0.08, 0.08, 0.08])
cons = [{'type': 'eq', 'fun': constraint1},
               {'type': 'ineq', 'fun': constraint2},
               {'type': 'ineq', 'fun': constraint3},
               {'type': 'ineq', 'fun': constraint4},
               {'type': 'ineq', 'fun': constraint5},]
print(minimize(Phi, method='BFGS', jac=grad, constraints=cons, bounds=bnds))

But I have " TypeError: minimize() missing 1 required positional argument: 'x0' ". And I havent information about x0. Is it correct minimization of function with constraints or its impossible to do this?

UPD

Result is

def Phi2(params):
    u0,u1,u2,u3,x0,x1,x2,x3 = params
    return -(1+u0*x0+u1*x1+u2*x2+u3*x3)


x0 = np.asarray([0,0,0,0,0,0,0,0])

def constraint1(params):
    u0,u1,u2,u3,x0,x1,x2,x3 = params
    return u0+u1+u2+u3-1.0


bnds = Bounds ([0,0,0,0,-0.08,-0.08,-0.08,-0.08,], [1,1,1,1,0.08, 0.08, 0.08])

cons = [{'type': 'eq', 'fun': constraint1}]
print(minimize(Phi2,x0, method='BFGS', constraints=cons, bounds=bnds))

But there is some problem. I have gradient for u0,u1,u2,u3 in numpy array 'grad'. How to use it correctly? If i do jac=grad in parametrs of minimize then result is

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

Also: BFGS does not support constraints. Consult the documentation. — Erwin Kalvelagen, Jan 19 '20 at 18:29

score 1 · Accepted Answer · answered Jan 19 '20 at 14:56

1

The scipy documentation says that x0 it is a positional argument and so it is required.

It says this about x0:

Initial guess. Array of real elements of size (n,), where ‘n’ is the number of independent variables.

It seems like you have to provide your initial guess at the minimum. Have you tried supplying an empty array?

answered Jan 19 '20 at 14:56

Sam Broster

542
5
15

When I add x0 (x0 = np.zeros(shape=(1,4))) to minimize, I have "TypeError: Phi() missing 1 required positional argument: 'X'" – Ильшат Мурзурбеков Jan 19 '20 at 16:20
Have you seen this example here: https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#nelder-mead-simplex-algorithm-method-nelder-mead – Sam Broster Jan 19 '20 at 17:21
The reason it is failing is that scipy expects `Phi` to be a function like: `fun(x, *args)` where `*args` is a list of constants but in you have `Phi(u, X)` where `X` is not constant. – Sam Broster Jan 19 '20 at 17:24
Do I understand correctly that such a function cannot be minimized? – Ильшат Мурзурбеков Jan 19 '20 at 17:47
1

It should be possible, this article gives some clues: https://stackoverflow.com/questions/13670333/multiple-variables-in-scipys-optimize-minimize I'll see I can make sense of it. – Sam Broster Jan 19 '20 at 17:52
Thank you it helped me a lot. But now I have little problem with gradient(updated post) – Ильшат Мурзурбеков Jan 19 '20 at 18:24
I don't understand the documentation for the constaints. When I provided this dummy function it worked: `grad = lambda x: np.zeros(shape=(1,4))` – Sam Broster Jan 19 '20 at 18:33

How to minimize function like this

1 Answers1