Python数值优化求解器
tests/test_trust_banana.py
Rosenbrock's banana function:
>>> import numpy
>>> from numpy import ndarray
>>> from optimizer import trust_region
>>> def func(_x: ndarray) -> float:
... x: float = float(_x[0])
... y: float = float(_x[1])
... return 100 * (y - x * x) ** 2 + (1 - x) ** 2
>>> def grad(_x: ndarray) -> ndarray:
... x: float = float(_x[0])
... y: float = float(_x[1])
... return numpy.array([-400 * (y - x * x) * x - 2 * (1 - x), 200 * (y - x ** 2)])
>>> n = 2
>>> constraints = (
... numpy.zeros((0, n)), # A
... numpy.zeros((0,)), # b
... numpy.full((n,), -numpy.inf), # lb
... numpy.full((n,), numpy.inf), # ub
... )
>>> opts = trust_region.Trust_Region_Options(max_iter=500)
>>> result = trust_region.trust_region(
... func,
... grad,
... numpy.array([-1.9, 2]),
... constraints,
... opts,
... )
<BLANKLINE>
...Iter...
>>> print(result.success, result.x)
True [1. 1.]tests/test_trust_neg_curv.py
>>> import math
>>> import numpy
>>> from numpy import ndarray
>>> from optimizer import trust_region
>>> def func(_x: ndarray) -> float:
... x: float = float(_x[0])
... return 1 / x + math.log(x)
>>> def grad(_x: ndarray) -> ndarray:
... x: float = float(_x[0])
... return numpy.array([1 / x - 1 / (x * x)])
>>> n = 1
>>> constraints = (
... numpy.zeros((0, n)), # A
... numpy.zeros((0,)), # b
... numpy.array([0.25]), # lb
... numpy.array([10.0]), # ub
... )
>>> opts = trust_region.Trust_Region_Options(max_iter=500)
>>> result = trust_region.trust_region(
... func,
... grad,
... numpy.array([9.5]),
... constraints,
... opts,
... )
<BLANKLINE>
...Iter...
>>> print(result.success, result.x)
True [0.99999985]