difference between Gurobi solution and Python Scipy nnls solution for non-negative least square problem
solve the non-negative least square problem
argmin_x || Ax - b ||_2 for x>=0
for python solution, simply call nnls function as
r,s= nnls(A, B);
for Gurobi solution, define as
A_dot_A = A.T.dot(A);
A_dot_B = A.T.dot(B);
b_dot_b = B.T.dot(B);
m = gp.Model("qp")
x = m.addMVar(shape=int(A.shape[1]), name="x")
obj = x @ (A_dot_A @ x -2.0*A_dot_B)
m.setObjective(obj,, GRB.MINIMIZE)
m.addConstr(x @ A_dot_A @ x -2.0*A_dot_B @ x + b_dot_b >= 0, "c0")
m.optimize()
results completely different, seems nnls gives the right solution while Gurobi not. any thoughts?
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Could you paste a full example with A and b? I just tried the small example from the scipy documentation and Gurobi gave me the same result as nnls.
Moreover, I don't think you need to add the constraint since it simply says that the Euclidean norm of Ax-b should be non-negative (which should always be true by definition). What do you think?
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Thank you for your response! My case is a non-convex optimization case.
A sample coefficient is in the link
https://drive.google.com/open?id=16v7_iQn3sVGumuIl9wsr0E3Nz3eC2SN3zUa_DBLW1Pg
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I already set the solver to be 'nonconvex' by
m.setParam("NonConvex", 2)
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