I'd like to solve the following optimization problem: Find non-negative scalar $a$, $b$, $c$ to minimize
$\| (D-(aA+bB+cC+D^{-1})^{-1})y\|^2+2\operatorname{trace}((aA+bB+cC+D^{-1})^{-1})$
where $A$,$B$,$C$ are known large sparse positive semi-definite matrices, $D$ is a known diagonal matrix with positive diagonal elements, and $y$ is a known column vector, and $\|\cdot\|$ denotes Euclidean norm.
Which optimization method or numerical method is the best (in terms of speed and complexity) to solve the problem?