Taking the power in objective function returns TypeError

[vpozdnyakov]

Describe the bug I cannot take the power in objective function. For example, I cannot minimize the variance of the set of variables.

To Reproduce

from mip import Model, MINIMIZE, BINARY, INTEGER
model = Model(sense=MINIMIZE)
a_list = [3, 4, 5]
x_list = [model.add_var(var_type=INTEGER) for _ in range(3)]
y_list = [a*x for a, x in zip(a_list, x_list)]
y_mean = sum(y_list) / len(y_list)
model.objective = sum([(y_mean - y)**2 for y in y_list]) / len(y)

TypeError: unsupported operand type(s) for ** or pow(): 'LinExpr' and 'int'

Expected behavior Here is no the error

Desktop (please complete the following information):

• Operating System, version: google colab
• Python version: google colab
• Python-MIP version: 1.14.2

[christian2022]

This is by design. MIP in fact is Mixed Integer linear Program. So all constraints and objective functions need to be linear. It looks like you're trying to solve a Minimum Least Squares Problem. Maybe it's an option to replace (y_mean - y)**2 by abs(y_mean - y), so "Least Absolute Deviation", which can be linearized by: y_dev = [model.addvar() for in y_list] mode.add_constr(y_dev[i] <= y_mean - y_list[i] for i in range(len(y_list))] mode.add_constr(y_dev[i] >= y_mean - y_list[i] for i in range(len(y_list))] model.objective = sum(y_dev)

[vpozdnyakov]

@christian2022 thank you!