Constrained optimization

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Matlab post

adapted from http://en.wikipedia.org/wiki/Lagrange_multipliers.

Suppose we seek to minimize the function \(f(x,y)=x+y\) subject to the constraint that \(x^2 + y^2 = 1\). The function we seek to maximize is an unbounded plane, while the constraint is a unit circle. We could setup a Lagrange multiplier approach to solving this problem, but we will use a constrained optimization approach instead.

from scipy.optimize import fmin_slsqp

def objective(X):
    x, y = X
    return x + y

def eqc(X):
    'equality constraint'
    x, y = X
    return x**2 + y**2 - 1.0

X0 = [-1, -1]
X = fmin_slsqp(objective, X0, eqcons=[eqc])
print X
Optimization terminated successfully.    (Exit mode 0)
            Current function value: -1.41421356237
            Iterations: 5
            Function evaluations: 20
            Gradient evaluations: 5
[-0.70710678 -0.70710678]

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