Scipy最小化成功终止，但不满足不等式约束

Question

我试图最小化函数0.5*（x^2+y^2）服从一系列（N=20）的不等式约束，形式为x a1+y a2+a3 z>；=1。溶液应在x=0.50251，y=-0.5846，z=0.36787左右。例程以消息“Optimization terminated successfully”终止，但超过一半的约束未得到遵守。我也尝试了不同的解决方案，结果是一样的。在

缩放目标函数会改变解，但不会收敛到预期的解。在

from scipy.optimize import minimize
import numpy as np


Pct=np.array([[-0.664,  3.179],[ 0.231, -2.044],[-2.493,  3.25 ],[ 0.497, -0.654],[-1.27,   1.248],[-1.185,  1.814],[-1.843,  4.386],[-1.616,  1.401],[ 0.052, -1.232],[-3.145,  0.404],[ 0.672, -1.655],[ 2.202, -1.888],[ 4.084, -1.067],[ 1.006, -1.671],[-2.255,  1.51 ],[-1.264,  1.663],[ 1.897, -2.217],[ 1.843, -1.276],[-1.693,  1.623],[ 2.297, -1.709]])
Sid=np.array([-1,  1, -1,  1, -1, -1, -1, -1,  1, -1,  1,  1,  1,  1, -1, -1,  1,  1, -1,  1])

# func to be minimized 
def OptFunc(x):
  return 0.5*(x[0]**2+x[1]**2)
def JacOptFunc(x):
  return np.array([x[0],x[1],0.0])  

# Constraints
c=[]
for i in range(len(Sid)):
  c+=[{'type': 'ineq', 'fun': lambda x:  Sid[i]*(x[0]*Pct[i,0]+x[1]*Pct[i,1]+x[2])-1 }]
cons=tuple(c)    

# start optimization
res = minimize(OptFunc,(0.3,-0.2,0.1),constraints=cons,method='SLSQP',jac=JacOptFunc)

#expected solution should be around
# [0.5025062702615434, -0.584685257866671, 0.36787016514022236]
print("-->",res.message)
print("solution ",res.x,flush=True)

print("Check Constraints")
cons=list(cons)
for i in range(len(cons)):
  lokfun=c[i]['fun']
  print("Constraint # ",i," value: ",lokfun(res.x))

预期结果就在附近 x=0.50251，y=-0.5846，z=0.36787 但我得到以下输出：

^{2}$

Answer 1

我对scipy.optimize知之甚少，但我可以发现一个问题

for i in range(len(Sid)):
  c+=[{'type': 'ineq', 'fun': lambda x:  Sid[i]*(x[0]*Pct[i,0]+x[1]*Pct[i,1]+x[2])-1 }]

问题是Python闭包是后期绑定的，这意味着每个约束中的i的值实际上是在循环完成后计算的。实际上，您实际上将相同（最后一个）约束施加了20次。见https://docs.python-guide.org/writing/gotchas/#late-binding-closures

可能的解决方案：

^{pr2}$

结果

 > Optimization terminated successfully.
solution  [ 0.52374351 -0.56495542  0.37021863]
Check Constraints
Constraint #  0  value:  0.7735403550593944
Constraint #  1  value:  0.6459722649608017
Constraint #  2  value:  1.7715790719554194
Constraint #  3  value:  8.137268636687622e-11
Constraint #  4  value:  -2.2235047136831554e-10
Constraint #  5  value:  0.27524657110337936
Constraint #  6  value:  2.0729351509689136
Constraint #  7  value:  0.2676534344356165
Constraint #  8  value:  0.09347837249122604
Constraint #  9  value:  0.5051967055706261
Constraint #  10  value:  0.6571754935710583
Constraint #  11  value:  1.5901376792721638
Constraint #  12  value:  2.1119945643862095
Constraint #  13  value:  0.8411451130595076
Constraint #  14  value:  0.6639056792092357
Constraint #  15  value:  0.23131403951409935
Constraint #  16  value:  1.6162662427554526
Constraint #  17  value:  1.0563610395273058
Constraint #  18  value:  0.43340178883510116
Constraint #  19  value:  1.5387662919992176