scipy.optimize.minimize_scalar() adding constraint to helper function result inside objective function?

Question

I have a function func_x() that I am trying to minimize using scipy.optimize.minimize_scalar().

func_x() also calls another function func_y() whose result func_x() uses in part to calculate the final scalar value. I want the optimization to also have a constraint on the value of func_y() such as a minimum or max value for func_y()'s result. In my future cases there may also be other helper functions, but the commonality is, given a scalar input x, they will also return a scalar value for func_x() to use.

from scipy.optimize import minimize_scalar
def func_y(x):
    return x^2-1/x
def func_x(x):
    return (x - 2) * func_y(x) * (x + 2)**2

res = minimize_scalar(func_x, bounds=(-10, 10), method='bounded')
res.x

Is there anyway to enforce a constraint like func_y(x) > 1 within scipy.optimize. minimize_scalar()?

I checked the documentation - I believe the bounds parameter only sets the optimization floor/ceiling for the scalar input x.

Based on user ekrall's suggestion, I also looked into scipy.optimize.minimize() with the usage of the constraints parameter

from scipy.optimize import minimize

def constraint1(x):
    return func_y(x)-1

con1 = {'type': 'ineq', 'fun': constraint1}

which should check that func_y(x) >= 1

It sounds like you are wanting to solve a constrained optimization having multiple constraints. scipy.optimize.minimize() allows you to pass in constraints. — ekrall, Jan 14 '22 at 03:24
I looked into it a little more and the other SO examples I found seem to concur. I'm just not sure whether the constraints would work for other types of helper/custom functions or if I was trying to use something like a linear regression model to generate the output of func_y() given x. — hamhung, Jan 14 '22 at 03:53

Bob · Answer 1 · 2022-01-14T12:55:48.700

I would also advice you to use minimize. You just have to be aware of the limitations

Constraints definition (only for COBYLA, SLSQP and trust-constr).

And also

Note that COBYLA only supports inequality constraints.

From this we conclude that either SLSQP or trust-constr must be choosen.

With trust-constr the results are fine

res = minimize(func_x, 5, method='SLSQP', bounds=[[-10, 10]], 
               constraints=[{'type': 'ineq', 'fun': lambda x: 1-func_y(x)}])
print(res.x, res.fun, func_y(res.x), res.success)
res = minimize(func_x, 5, method='SLSQP', bounds=[[-10, 10]], 
               constraints=[{'type': 'ineq', 'fun': lambda x: func_y(x)-1}])
print(res.x, res.fun, func_y(res.x), res.success)
res = minimize(func_x, 5, method='SLSQP', bounds=[[-10, 10]])
print(res.x, res.fun, func_y(res.x), res.success)

gives

[1.32467216] [-7.4635986] [0.99985257]
[1.59008719] [-10.0354401] [1.89948096]
[1.59008719] [-10.0354401] [1.89948093]

However this type constraints are not working properly for SLSQP.

Another way to represent constraints is as NonlinearConstraint or LinearConstraint, in that case SLSQP works fine

res = minimize(func_x, 5, method='trust-constr', bounds=[[-10, 10]], 
               constraints=[NonlinearConstraint(func_y, lb=1, ub=1.5)])
print(res.x, res.fun, func_y(res.x))
res = minimize(func_x, 5, method='SLSQP', bounds=[[-10, 10]], 
               constraints=[NonlinearConstraint(func_y, lb=1, ub=1.5)])
print(res.x, res.fun, func_y(res.x))

gives

[1.47559988] [-9.50009675] [1.49970451]
[1.47568652] [-9.50087235] [1.5]

An important detail is that the constraint func_y(x) > 1 splits your domain in two parts, the objective function is better on the left, but the method will probably only explore the part on the right.

scipy.optimize.minimize_scalar() adding constraint to helper function result inside objective function?

1 Answers1