I am attempting to use a constrained quadratic optimization to find the coefficients of a reproducing kernel.
The problem is as follows:
$y(t)=\sum_{i=0}^J\alpha_iK(t, t_i)$
$Q(\alpha)= \alpha^tK\alpha$
The optimization problem looks like this:
Minimize $Q(\alpha)$ such that, $Gx <= h$, $Ax = b$
Trying to optimize this using different optimizers(CVXOPT, MOSEK, Scipy) all fail. MOSEK gives the only decent error message, "Primal Infeasible". I don't agree with that given that I know RKHS have unique solutions.
Some things I have checked:
- My kernel matrix is positive definite and symmetric.
- The cost function or $Q(\alpha)$ is always positive.
- My constraint matrices are not full rank (Mosek has a pre-solve that supposedly removes redundant constraints)
I am as sure as possible that I have setup my problem correctly. I am just unsure of what I can do from here to check myself.
Does anyone have any other ways I can possibly figure out where my problem is?