I have implemented a convex optimization algorithm based on the ADMM approach for quadratic programming of the form below:
$$ \begin{array}{ll} \text{minimize} & x^T Q x + px\\ \text{subject to} & Ax + b = 0\\ \text{ } & Dx + E <=0\end{array}$$
the problem is that when some of the inequalities become active in the optimal solution, ADMM get too slow and actually it can't find the active ones, I thought it might be caused by ill-scaled matrices and I used a preconditioning method from "An Operator Splitting Solver for Quadratic Programs" article, but nothing changed and it still cannot find active inequalities. I have used Active-Set method to polish the solution obtained by the ADMM method, but as the active set is not known after running the ADMM algorithm it takes too many iterations to reach the optimal solution, Do you know any method other than the Active-Set method for polishing the solution?