我试图最小化函数（函数的积分），给定约束
def s(y,a,b,c,d):
v = [1, y, y**2, y**3]
alpha = [a, b, c, d]
q = np.inner(v,alpha)
return -q*np.exp(-q)
def p(y,a,b,c,d):
v = [1, y, y**2, y**3]
alpha = [a, b, c, d]
q = np.inner(v,alpha)
return np.exp(-q)
def Q(u):
a, b, c, d = u
d = integrate.quad(lambda y: s(y,a,b,c,d), 0, 1)
return d[0]
cons = ({'type': 'eq', 'fun' : integrate.quad(lambda y: p(y,a,b,c,d), 0, 1)[0]-1},
{'type': 'eq', 'fun' : integrate.quad(lambda y: (p(y,a,b,c,d)*y), 0, 1)[0]-0.483523521402009},
{'type': 'eq', 'fun' : integrate.quad(lambda y: (p(y,a,b,c,d)*y**2), 0, 1)[0]-0.300458990347083},
{'type': 'eq', 'fun' : integrate.quad(lambda y: (p(y,a,b,c,d)*y**3), 0, 1)[0]-0.209996591802522})
res = minimize(Q, x0 = (0, 0, 0, 0), method='BFGS', constraints=cons)
print(res)
我得到了一个输出
fun: -0.36787942624169967
hess_inv: array([[ 17.98311921, -49.74794121, 2.50822967, 36.21942131],
[ -49.74794121, 191.70720321, -23.14586623, -158.65310285],
[ 2.50822967, -23.14586623, 8.1640543 , 25.72129091],
[ 36.21942131, -158.65310285, 25.72129091, 142.59127393]])
jac: array([ -3.54647636e-06, -1.94460154e-06, -1.75461173e-06,
3.24100256e-07])
message: 'Optimization terminated successfully.'
nfev: 126*
*nit: 19
njev: 21
status: 0
success: True
x: array([ 0.99920744, 0.0092224 , -0.02276881, 0.0150456 ])**
然而，使用这个X数组，不满足约束
x = (0.99920744, 0.0092224 , -0.02276881, 0.0150456)
integrate.quad(lambda y: p(y,x[0],x[1],x[2],x[3]), 0, 1)[0]
0.3678829742546207
不是1，如约束中具体说明的那样。当它显然没有收敛时，它如何声称收敛？