设计一个python程序通过鲍威尔算法进行一个6参数的非线性优化
时间: 2023-02-26 19:04:28 浏览: 42
好的,下面是一个实现鲍威尔算法的简单Python程序:
```
import numpy as np
from scipy.optimize import minimize
def powell(func, x0, args=(), xtol=1e-8, ftol=1e-8, maxiter=None, maxfun=None,
full_output=False, disp=False, retall=False, callback=None):
"""Minimize a function using modified Powell's method.
Optimize the function, `func`, whose gradient is not available, using a
modification of Powell's conjugate direction method. The algorithm uses
the technique of backtracking along the search direction to ensure
convergence.
"""
x0 = np.asarray(x0).flatten()
fcalls, func = wrap_function(func, args)
x = x0
if retall:
allvecs = [x0]
N = len(x0)
rank = N
if maxiter is None:
maxiter = N * 200
if maxfun is None:
maxfun = N * 200
if rank == 0:
return optimize.OptimizeResult(fun=func(x0), x=x0, nit=0,
nfev=fcalls[0], success=True)
R = np.eye(N, dtype=int)
for k in range(rank):
d = R[k]
x1 = x + d
fx = func(x1)
fx2 = fx
loop_again = True
i = 0
while loop_again and i < maxiter:
if fx2 > fx:
t = 2 * (fx2 - 2 * fx + func(x - d))
t = t * (fx2 - fx - t) / (2 * t ** 2)
if t < 0:
t = min(2 * (fx2 - fx) / t, 0.1 * np.abs(x1 - x))
else:
t = 0.1 * np.abs(x1 - x)
x1 = x + t * d
fx2 = func(x1)
if fx > fx2:
x = x1
fx = fx2
i += 1
else:
loop_again = False
d = x1 - x
x = x1
if retall:
allvecs.append(x)
if callback is not None:
callback(x)
if k < rank - 1:
for j in range(k, N):
R[j, k] = np.dot(R[j], d)
for j in range(k + 1, N):
R[k, j] = 0.
return optimize.OptimizeResult(fun=fx, x=x, nit=i, nfev=fcalls[0], success=True)
```
这个程序实现了一个