from scipy.optimize import basinhopping, rosen
def build_show_bh(MIN=None):
    if MIN is None:
        MIN = [0]
    def fn(xx, f, accept):
        if f < MIN[-1]:
            print([round(x, 2) for x in xx], f)
            MIN.append(f)
    return fn
x0 = (0.4, 0.6, 0.8)
bounds = [(0,1)]*3
minimizer_kwargs = dict(method="L-BFGS-B", bounds=bounds)
progress_f = [0]
c = build_show_bh(progress_f)
print("Optimizing using basinhopping")
res = basinhopping(
    rosen, 
    x0,
    minimizer_kwargs=minimizer_kwargs,
    niter=10,
    callback=c, 
    disp=True
)
print(f"external way of keeping track of MINF: {progress_f}")

# 我会通过创建一个关于连续值之间差异的约束来解决这个问题。
def constraint(x, use_epsilon=True):
    difference_between_coeffs = np.diff(x)
    epsilon = 1e-6  # 使用此值使约束稍微保守一些
    min_difference = 0.1 + (epsilon if use_epsilon else 0)
    difference_metric = difference_between_coeffs - min_difference
    difference_metric_capped = np.minimum(0, difference_metric)
    return np.sum(difference_metric_capped)
# 注意：此约束还要求系数按排序顺序排列。
# 写这个程序时，我遇到的问题是，有时SLSQP会给我一些稍微违反约束的点，我通过要求点之间稍微远一些来解决了这个问题。我发现`epsilon = 1e-6`足以解决这个问题。
# 然后，您必须告诉最小化器使用此约束：
constraints = [
    {"type": "eq", "fun": constraint}
]
minimizer_kwargs = dict(method="SLSQP", bounds=bounds, constraints=constraints)
# 注意：我将方法从L-BFGS-B切换到SLSQP，因为BFGS不支持约束。您还可以使用trust-constr - 这是唯一支持约束和边界的其他方法。
# 接下来，我遇到的问题是，有时候basinhopping选择了一个违反约束的点，这导致了最小化的失败，然后认为basinhopping选择的点是正确的。我通过为basinhopping使用接受测试来解决了这个问题。这样，如果点违反了约束，就不会接受这些点。
def accept(x_new, **kwargs):
    return constraint(x_new) == 0
res = basinhopping(
    # ...
    accept_test=accept,
)
# 完整代码：
from scipy.optimize import basinhopping, rosen
import numpy as np
def build_show_bh(MIN=None):
    if MIN is None:
        MIN = [0]
    def fn(xx, f, accept):
        if f < MIN[-1]:
            print([round(x, 2) for x in xx], f)
            MIN.append(f)
    return fn
def constraint(x, use_epsilon=True):
    difference_between_coeffs = np.diff(x)
    epsilon = 1e-6  # 使用此值使约束稍微保守一些
    min_difference = 0.1 + (epsilon if use_epsilon else 0)
    difference_metric = difference_between_coeffs - min_difference
    difference_metric_capped = np.minimum(0, difference_metric)
    return np.sum(difference_metric_capped)
def accept(x_new, **kwargs):
    return constraint(x_new) == 0
constraints = [
    {"type": "eq", "fun": constraint}
]
x0 = (0.4, 0.6, 0.8)
bounds = [(0, 1)] * 3
minimizer_kwargs = dict(method="SLSQP", bounds=bounds, constraints=constraints)
progress_f = [100]
c = build_show_bh(progress_f)
print("Optimizing using basinhopping")
res = basinhopping(
    rosen,
    x0,
    minimizer_kwargs=minimizer_kwargs,
    accept_test=accept,
    niter=10,
    callback=c,
    disp=True
)
print(f"external way of keeping track of MINF: {progress_f}")