# 72

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58``` ```import seaborn as sb import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D import numpy as np from scipy.optimize import minimize from sklearn.cluster import KMeans def pos(x): if x > 0: return x return 0 def f1(x): return 2*x[0]**2 + 3*x[0]*x[1] - 4.0*x[1]**2 - 5.0*x[0] - x[1] #return 2.0*x[0]**2 + 4.0*x[0]*x[1] + x[1]**2 - x[0] - 5.0*x[1] def f2(x): return 2.0*(x[0]-2)**2 + (x[1]-5)**2 + 2.0*x[2]**2 #return 4.0*(x[0]-3)**2 + (x[1]-5)**2 + 3.0*x[2]**2 def g1(x): return x[0] - x[1] + 3*x[2] - 6 #return x[0] + x[1] + 2.0*x[2] - 16 def g2(x): return 3.0*x[1] - 2.0*x[0] - 12 #return -2.0*x[0] + x[1] + x[2] - 10 arr0 = [0.0, 0.0, 0.0] arr1 = minimize(lambda alpha: f1(alpha), arr0, method='nelder-Mead').x print arr1 arr2 = minimize(lambda alpha: f2(alpha), arr0, method='nelder-Mead').x print arr2 vect1 = np.array([0.89, 0.44]) vect2 = np.array([1.2, 1.0]) vect3 = np.array([1.0, 1.0]) vect4 = np.array([0.66, 1.0]) eps = 0.01 def Sh(arr0, gap, it, vect): def F(alpha, r): return (vect[0]*(f1(alpha) - f1(arr1)) + vect[1]*(f2(alpha) - f2(arr2)) + (r/2.) * ((pos(g1(alpha)) ** 2) + (pos(g2(alpha)) ** 2))) def P(x, r): return ((r/2.) * ((pos(g1(x)) ** 2) + (pos(g2(x)) ** 2))) res = (minimize(lambda alpha: F(alpha, gap), arr0, method='SLSQP')) x1 = res.x if np.fabs(P(x1, gap)) <= eps: print 'it: ', it return x1 else: return Sh(x1, 5.0 * gap, it+1, vect) def start(vect): print 'Sh:' result = Sh([0.0, 100.0, 0.0], 1.0, 0, vect) print 'x=', result, 'f1(x)=', f1(result), 'f2(x)=', f2(result) start(vect1) start(vect2) start(vect3) start(vect4) ```