I have a convex optimization problem of finding a function Q(x,y) as below:

Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the question, so I'm skipping them. The function $k(x,y)$ is known and my aim is to find the form of $Q(x,y)$. I was thinking if I could represent this double integration as a matrix multiplication and I convexly minimize over the unknown matrix of $Q(i,j)$ values, then I can curve fit or do something from the values available. My question is how do I represent a double integral as a matrix multiplication? Say, the limits are (-10,10) for both variables' integration.