The following example is adapted from a textbook on operations research:
#Ronald L. Rardin. "Optimization in Operations Research."
# Prentice-Hall, Upper Saddle River, NJ, 1998. Example 14.3, p. 792
# Global constants
d1 = 2.5
d2 = 40
t1 = 0.6
t2 = 1.0
p0 = 200
initial_guess = [20, 500]
def x3(x):
return 36.25 * (d2 - x[0]) * (t2 - t1) / t1 * log(x[1] / p0)
def x4(x):
return 348300 * (d2 - x[0]) * (t2 - t1)/ x[1]
def f(x):
return 61.8 + 5.72 * x[0] + 0.0175 * x3(x)^0.85 + \
0.0094 * x4(x)^0.75 + 0.006 * t1 * x3(x)
c_1 = lambda p: p[0]
c_2 = lambda p: p[1]
c_3 = lambda p: t2 * p[0] - d1 * t1 - d2 * (t2 - t1)
c_4 = lambda p: p[1] - p0
(x1, x2) = minimize_constrained(f, [c_1,c_2,c_3,c_4], initial_guess)
print('x1 = {0}'.format(x1))
print('x2 = {0}'.format(x2))
print('x3 = {0}'.format(x3([x1,x2])))
print('x4 = {0}'.format(x4([x1,x2])))
print('x5 = {0}'.format(f([x1,x2])))The fitted values are:
