如何通过 pytorch 有效地求解二次方程组？

Question

我需要求解如下所示的非线性方程组：

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

C的尺寸约为10，这个方程组最多可以求解十亿次，所以用torch实现很好，所以可以使用GPU。 有没有比梯度下降更好的方法？

Answer 1

PyTorch 仅原生支持求解线性方程组（例如torch.solve 、 torch.linalg.solve ）。 但是您可以尝试例如：

轨迹实验室/qpth

PyTorch 的快速且可微分的 QP 求解器。

• https://locuslab.github.io/qpth/