scipy.minimize constrained optimization problem with multiple variables

Question

I am currently trying to implement the following optimization problem in python (in order to resolve it with scipy.optimize.minimize).

Please note that alpha is given,T is the number of generated random values (i.e. via Monte Carlo simulation, also given), z is an array of artificial variables (ignore the last constraint). The function f(x,y) is equal to -y.T * x (y is an array of nT random values). Variable val is a pandas data frame with all the observed data. Variable r is the realization of the random events (randomly generated using MonteCarlo technique - fitting a distribution, pandas nT).

Unfortunately I am facing different problems while truing to solve it. Can anyone be so kind to help me to code it correctly?

EDIT: following the modified code with correct init and constraints. I am not able to figured out how to write correctly the bounds (for x[0] bounds should be (0, None), for x1 and x[2] bounds should be (None, None). Can anyone be so kind to suggest me the correct way?

def objective(x, alpha, t):
    #
    return x[1] + (1 / (1 - alpha) * t) * np.sum(x[2])

def problem(val, t = 10, alpha = 0.9):
    #
    y = []
    
    for simbolo in val.columns:
        loc, scale = sts.gumbel_l.fit(val[simbolo])
        y.append(sts.gumbel_l.rvs(loc, scale, t))
        
    init = np.array(([1 / len(val.columns)] * len(val.columns), [1] * t, [0] * t))
    constraints = [
        {"type": "ineq", "fun": lambda x: x[2]},
        {"type": "ineq", "fun": lambda x: np.dot(x[0].T, np.asarray(y)) + x[1] + x[2]}
        ]
    bounds = ((0, None),) * len(val.columns)
    args = (alpha, t)
        
    res = opt.minimize(
        objective,
        x0 = init,
        args = args,
        bounds = bounds, 
        constraints = constraints
    )
    
    return res['x']

I tried to write the bounds as follow:

bounds = (((0, None),) * len(var.columns), ((None, None),) * len(var.columns), ((None, None),) * len(var.columns))

by I get the following error:

 File "main.py", line 250, in 
    problem(r)
  File "port.py", line 152, in vanilla_cvar
    res = opt.minimize(
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/scipy/optimize/_minimize.py", line 625, in minimize
    return _minimize_slsqp(fun, x0, args, jac, bounds,
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/scipy/optimize/slsqp.py", line 315, in _minimize_slsqp
    new_bounds = old_bound_to_new(bounds)
  File "/Library/Frameworks/Python.framework/Versions/3.8/lib/python3.8/site-packages/scipy/optimize/_constraints.py", line 316, in old_bound_to_new
    lb, ub = zip(*bounds)
ValueError: too many values to unpack (expected 2)

scipy.minimize constrained optimization problem with multiple variables

0 Answers