# Optimization problem

In the expression:

$${\underset{\Omega}{\min}\left\|\beta A\Omega^{-1}B+C\right\|_{F}^{2}+tr(W\Omega^{-1}W^T)},$$ s.t. $${tr(\Omega)=1, \Omega \ge 0}$$, where any element of $${\Omega}$$ is nonnegative.

How to solve the variable $$\Omega$$?

• Does $\Omega \ge 0$mean that elements of $\Omega$ are nonnegative elementwise, or that $\Omega$ is positive semidefinite? Jul 14 at 17:30
• Are you minimizing that expression? You need to say so (edit the question). Jul 14 at 18:35
• yes, this is a minimization problem, and ${\Omega}$ is a symmetric matrix and any element of Ω is nonnegative. Jul 14 at 23:54
• There are many issues with this post, but if we can fix'em, it is an interesting question. Is $\Omega$ full or is there a fixed sparsity pattern? This looks like a sparse approximate inverse problem, and it is clear that if $\Omega$ is full then this is very expensive to solve. Jul 15 at 0:25
• Yes, in fact, ${\Omega \in R^{c \times c}}$ and ${\Omega}$ has the full rank. Jul 15 at 0:43