Scipy.optimize can't get correct answer when objective is Piecewise Linear Function and Equality Constraint

Question

I'm encountering a puzzling issue with SciPy's minimize function in a constrained optimization problem. My objective is to optimize a piecewise linear function with an equality constraint. However, the solution provided by the algorithm is different from what I logically expect. I would appreciate guidance on identifying the cause of this discrepancy and how to rectify it. Here's the relevant section of my Python code:

from scipy.optimize import minimize

def f(x):
    if 0 <= x <= 150:
        return x
    elif x >= 150:
        return 150

def objective(x):
    x1, x2 = x
    return f(x1 + 350) + f(x2)

def constraint(x):
    return x[0] + x[1] - 300

x0 = [0, 900]
bounds = [(0, 300), (0, 300)]
con = {'type': 'eq', 'fun': constraint}

result = minimize(objective, x0, bounds=bounds, constraints=con, options={'disp': True})

The output is

Optimization terminated successfully (Exit mode 0) Current function value: 300 Iterations: 1 Function evaluations: 3 Gradient evaluations: 1 (array([ 0., 300.]), 300)

The optimizer returns [0, 300] as the solution with a function value of 300. However, I was expecting [300, 0] to be the correct solution. This is based on the logic that f(x1 + 350) should max out first before x2 is increased, given the nature of the piecewise function f(x).

Answer 1

You are trying to minimize a concave function, and minimize finds only a local minimum. To find a global minimum, use one of the methods under "Global optimization" here: https://docs.scipy.org/doc/scipy/reference/optimize.html#