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我想用有界约束和线性不等式约束（即总和 wi*xi ≤ b）来解决约束最小化。然而，目标函数的 Hessian 矩阵可能是奇异的。

我已经用方法尝试了minimizeinscipy.optimize模块SLSQP，但没有运气。一个简化的问题如下：

In [1]: import scipy as sp
In [2]: from scipy.optimize import minimize
In [3]: H = sp.array([[  3.06235015e+04,   3.41413089e-01,   1.46545768e-01, 3.11691235e-01,   3.63587681e-01,   8.42621390e-01],
   ...:               [  3.41413089e-01,   6.97707374e-06,   3.43111013e-06, 6.83141186e-06,   6.88528951e-06,   1.00469425e-05],
   ...:               [  1.46545768e-01,   3.43111013e-06,   1.89088856e-06, 3.57752861e-06,   3.49362491e-06,   4.60245212e-06],
   ...:               [  3.11691235e-01,   6.83141186e-06,   3.57752861e-06, 7.39833538e-06,   6.97480991e-06,   9.41369621e-06],
   ...:               [  3.63587681e-01,   6.88528951e-06,   3.49362491e-06, 6.97480991e-06,   7.25710942e-06,   1.06384396e-05],
   ...:               [  8.42621390e-01,   1.00469425e-05,   4.60245212e-06, 9.41369621e-06,   1.06384396e-05,   3.46765772e-05]])

In [4]: fun = lambda x: sp.dot(sp.dot(x, H), x)   
In [5]: jac = lambda x: 2 * sp.dot(H, x)
In [6]: x0 = sp.array([-1, 0, 0, 0, 0, 0])
In [7]: bounds = [(-100, -1), (0, 100000), (0, 100000), (0, 100000), (0, 100000), (0, 100000)]

In [8]: res = minimize(fun, x0, method='SLSQP', jac=jac, bounds=bounds)
In [9]: res.x
Out[9]: array([-1.,  0.,  0.,  0.,  0.,  0.])

In [10]: fun(res.x)
Out[10]: 30623.501499999998

In [11]: fun([-1, 1000, 0, 0, 0, 0])
Out[11]: 29947.652395739999

In [12]: sp.__version__
Out[12]: '0.14.0'

我们可以看到优化器给出了错误的结果。是否有任何 python 模块可以满足要求？谢谢。

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