How can I efficiently solve a quaduatic equation system via pytorch?

Question

I need to solve a non-linear equation system shown below:

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

The dimention of C is about ten, and this equation system would be solved up to a billion of times, so it's nice to be implemented via torch so GPU could be utilized. Is there any methods better than gradient descent?

Answer 1

PyTorch only natively supports solving systems of linear equations (eg torch.solve , torch.linalg.solve ). But you can try eg:

locuslab/qpth

A fast and differentiable QP solver for PyTorch.

• https://locuslab.github.io/qpth/