Scipy.optimize.minimize SLSQP with linear constraints fails

Question

Consider the following (convex) optimization problem:

minimize 0.5 * y.T * y
s.t.     A*x - b == y

where the optimization (vector) variable

Answer 1

You've run into the "late binding closures" gotcha. All the calls to cons_i are being made with the second argument equal to 19.

A fix is to use the args dictionary element in the dictionary that defines the constraints instead of the lambda function closures:

cons_per_i = [{'type':'eq', 'fun': cons_i, 'args': (i,)} for i in np.arange(m)]

With this, the minimization works:

In [417]: sol2 = minimize(obj, x0 = z0, constraints = cons_per_i, method = 'SLSQP', options={'disp': True})
Optimization terminated successfully.    (Exit mode 0)
            Current function value: 2.1223622086
            Iterations: 6
            Function evaluations: 192
            Gradient evaluations: 6

You could also use the the suggestion made in the linked article, which is to use a lambda expression with a second argument that has the desired default value:

cons_per_i = [{'type':'eq', 'fun': lambda z, i=i: cons_i(z, i)} for i in np.arange(m)]