Is there an open-source alternative to MATLAB's fmincon function for constrained linear optimization? I'm rewriting a MATLAB program to use Python / NumPy / SciPy and this is the only function I haven't found an equivalent to. A NumPy-based solution would be ideal, but any language will do. 

 Answers:

An open-source alternative to MATLAB's fmincon function is scipy.optimize.minimize in the scipy library of Python. It provides a range of optimization algorithms, including the sequential least squares programming (SLSQP) algorithm, which can handle non-linear constraints and objectives.

Here's an example usage of minimize for minimizing a multi-variable objective function subject to constraints: 

import numpy as np
from scipy.optimize import minimize

def objective(x):
    return x[0]*x[3]*(x[0]+x[1]+x[2])+x[2]

def constraint1(x):
    return x[0]*x[1]*x[2]*x[3]-25.0

def constraint2(x):
    sum_sq = 40
    for i in range(4):
        sum_sq = sum_sq - x[i]**2
    return sum_sq

x0 = [1,5,5,1]

b = (1.0,5.0)
bnds = (b, b, b, b)

con1 = {'type':'ineq','fun':constraint1}
con2 = {'type':'eq','fun':constraint2}

cons = [con1,con2]

sol = minimize(objective,x0,method='SLSQP',bounds=bnds,constraints=cons)

print(sol.x)

Note that minimize may not be as efficient as fmincon for large-scale optimization problems, but it provides a good starting point for small to medium-sized problems. Additionally, scipy offers a wide range of other optimization and numerical methods that may be useful in various scenarios.