Python 如何通过Pytork有效地求解四元方程组？

我需要解一个非线性方程组，如下所示：

def trySolveEquation(V, L):
    #The equation to solve is:
    #{     (V . Ct) ^ 2 = 1
    #{     (L + u) . Ct = 0
    #C and u are the unknowns, C is a vector and u is a scalar, Ct is a vector transposed from C.
    #V is a vector with dimension equal to Ct, L is a square matrix, they are known.
    #u is Lagrange multiplier, and it's unknown.
    #'.' means matrix multiply.

    dim = V.shape[0]
    assert L.shape[0] == dim and L.shape[1] == dim
    C = torch.zeros((dim))
    Ct = C.view((dim, 1))
    u = 0

    '*Solve the equation here.*'

    print('C=', C)
    print('u=', u)
    return C, u

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C的尺寸大约是10，这个方程组将被求解多达10亿次，所以通过torch实现它很好，这样GPU就可以被利用。有什么方法比梯度下降法更好吗？

PyTorch只在本机上支持求解线性方程组（例如

torch.solve

，

torch.linalg.solve

）。但是你可以试试，例如：

房间板/qpth Pytork的快速可微QP求解器

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谢谢您的回答。您建议的包不支持二次约束，但我的问题是二次约束，所以它似乎没有帮助。是否有其他支持解决QCQP的软件包？