线性规划scipy.optimize.linprog

示例一：

import numpy as np
import matplotlib.pyplot as mpl
from scipy import optimize
c=np.array([3,1])
a=np.array([[2,1],[1,1]])
b=np.array([1,1])

res=optimize.linprog(-c,A_ub=a,b_ub=b,bounds=((0,None),(0,None)))

'''
    max z = 3x+y
    2x+y<=1  , A_ub[0]=[2,1], b_ub[0]=1
    x+y<=1   , A_ub[1]=[1,1],b_ub[1]=1
    x>=0,y>=0 , (0,None)->(0,+无穷)
    //若2x+y=3, 则A_eq=[2,1], b_eq=[3]
'''

print (res.x)
print (res.fun) #res.fun可能受函数传入参数-c的影响，需要取反才是所求最大值

示例二：
$min -7x_1+7x_2-2x_3-x_4-6x_5$
$3x_1-x_2+x_3-2x_4=-3$
$2x_1+x_2+x_4+x_5=4$
$-x_1+3x_2-3x_4+x_6=12$
$x_1>=0 ... x_6>=0$

import numpy as np
import matplotlib.pyplot as mpl
from scipy import optimize
c=np.array([-7,7,-2,-1,-6,0])
a=np.array([[3,-1,1,-2,0,0],[2,1,0,1,1,0],[-1,3,0,-3,0,1]])
b=np.array([-3,4,12])

res=optimize.linprog(c,A_eq=a,b_eq=b,bounds=((0,None),(0,None),(0,None),(0,None),(0,None),(0,None)))

print (res.x)
print (res.fun)

参考网站：
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html#scipy.optimize.linprog
scipy.optimize.linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None, method=’simplex’, callback=None, options=None)