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Convex approximation of an expression with fraction for CVX

I have the optimization problem $$\underset{\mathbf{x} \in \Bbb C^N}{\max} \left| \frac{\mathbf{x}a-b}{\mathbf{x}c+b} \right|^2$$ where $a$, $b$ and $c$ are some scalars. I want to solve this ...
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Convex approximation of an expression

I am trying to transform an expression given by $$ \operatorname{trace} \left( {\bf{X} } \right) + \left( \sum_{n=1}^N \mathcal{R}(x_n) \right) $$ into convex from where $\mathbf{x}$ is complex in ...
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