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python - scipy中约束中具有不完整伽马函数的非线性优化

问题描述

我想用 scipy (python3) 解决以下优化问题： 在此处输入图像描述

其中 I[.,.] 是“不完整的 gamma 函数”（scipy.special.gammainc）

我遵循了 scipy 优化指南并提出了以下代码：

from scipy.special import gammainc
from scipy.optimize import NonlinearConstraint
from scipy.optimize import BFGS
from scipy.optimize import minimize
import numpy as np

q = 200
k = 1.5625
alpha = 0.03125


def func(s):
    return s


def constraints(s):
    return q - k/alpha * (gammainc(k+1, s*alpha) + gammainc(k+1, (s+q)*alpha)) + s*gammainc(k, s*alpha) + (s+q)*gammainc(k, (s+q)*alpha)

nonlinear_constraint = NonlinearConstraint(constraints, -np.inf, 10.0, jac='2-point', hess=BFGS())

s0 = 1000
res = minimize(func, s0, method='trust-constr', jac='2-point', hess=BFGS(), constraints=[nonlinear_constraint], options={'verbose': 1})

print(res.x)

当我运行代码时，我得到这个（错误）输出：

/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_hessian_update_strategy.py:187: UserWarning: delta_grad == 0.0. Check if the approximated function is linear. If the function is linear better results can be obtained by defining the Hessian as zero instead of using quasi-Newton approximations.
  'approximations.', UserWarning)
Traceback (most recent call last):
  File "s_opt.py", line 23, in <module>
    res = minimize(func, s0, method='trust-constr', jac='2-point', hess=BFGS(), constraints=[nonlinear_constraint], options={'verbose': 1})
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_minimize.py", line 622, in minimize
    callback=callback, **options)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_trustregion_constr/minimize_trustregion_constr.py", line 519, in _minimize_trustregion_constr
    factorization_method)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_trustregion_constr/tr_interior_point.py", line 329, in tr_interior_point
    factorization_method, trust_lb, trust_ub, subprob.scaling)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_trustregion_constr/equality_constrained_sqp.py", line 121, in equality_constrained_sqp
    lb_t, ub_t)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_trustregion_constr/qp_subproblem.py", line 499, in projected_cg
    r = Z.dot(H.dot(x) + c)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/sparse/linalg/interface.py", line 415, in dot
    return self.matvec(x)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/sparse/linalg/interface.py", line 229, in matvec
    y = self._matvec(x)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/sparse/linalg/interface.py", line 527, in _matvec
    return self.__matvec_impl(x)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/optimize/_trustregion_constr/projections.py", line 193, in null_space
    aux2 = scipy.linalg.solve_triangular(R, aux1, lower=False)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/linalg/basic.py", line 336, in solve_triangular
    b1 = _asarray_validated(b, check_finite=check_finite)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/scipy/_lib/_util.py", line 246, in _asarray_validated
    a = toarray(a)
  File "/home/andreasziegler/miniconda3/lib/python3.7/site-packages/numpy/lib/function_base.py", line 499, in asarray_chkfinite
    "array must not contain infs or NaNs")
ValueError: array must not contain infs or NaNs

这告诉我我做错了什么。这是我第一次在 scipy 中使用优化器，因此很有可能我误解了一些东西（必要的）。我很高兴有任何提示。

标签： pythonscipyscipy-optimize-minimize

解决方案

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