# Doubt regarding principled approach towards approximating the Hessian

In my optimization problem, the hessian has a structure such that it can be written as the sum of two matrices. Populating the first of the matrices is efficient. Populating the second one is computationally very heavy and practically makes methods like truncated Newton useless. However, the second matrix is block diagonal in nature. I am thinking I will use a Quasi-Newton approximation to the second matrix and compute the first matrix exactly. Hence, get an approximation for the hessian by adding these two matrices. Intuitively, this Hessian approximation should be better than having a Quasi-Newton approximation for the entire Hessian matrix. Is this thinking correct? Have people successfully tried such an approach before and got a better optimization approach than a direct Quasi-Newton based approach?

• You're not likely to get a good theoretical answer to a question like this. Try it on your problem and see how well it works in practice. Commented Sep 16, 2016 at 14:05
• ok. I will try and see.
– Hari
Commented Sep 16, 2016 at 14:12