I am looking into the following optimization problem
$$\begin{array}{ll} \underset{\Delta X}{\text{minimize}} & trace(\Delta X^H \Delta X)\\ \text{subject to} & (X+\Delta X)'Q(X + \Delta X) \succeq Q\end{array}$$
where $Q$ is a positive matrix (complex Hermitian), and $X$, $\Delta X$ are complex diagonal matrices.
What is the state of art in solving such problems? I am hoping for something simpler than the generic convex-concave procedure (CCP), e.g., the approach outlined in
- Xinyue Shen, Steven Diamond, Yuantao Gu, Stephen Boyd, Disciplined Convex-Concave Programming, April 2016.