a concave function of $\m{R}$ on the positive semidefinite cone [@boyd2004convex]. It follows that the problem in is nonconvex and no efficient algorithms can guarantee to obtain the global optimizer. A popular locally convergent approach to minimization of such a concave $+$ convex function is the majorization-maximization (MM) algorithm (see, e.g., [@fazel2003log]). Let $\m{u}_j$ denote the $j$th iterate of the optimization variable $\m{u}$. Then, at the $\sbra{j+1}$th iteration we replace $\ln\abs{T\sbra{\m{u}}+\epsilon\m{I}}$ by its tangent plane at the current value $\m{u}=\m{u}_j$: where $c_j$ is a constant independent of $\m{u}$. As a result, the optimization problem at the $\sbra{j+1}$th iteration becomes Since $\ln\abs{T\sbra{\m{u}}+\epsilon\m{I}}$ is strictly concave in $\m{u}$, at each iteration its value decreases by an amount greater than the decrease of its tangent plane. It follows that by iteratively solving the objective function in (\[formu:problem\]) monotonically decreases and converges to a local minimum.

Interpretation as RAM  {#sec:WAN_SDP}
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To interpret the optimization problem in (\[formu:problem\_j\]), let us define a weighted continuous dictionary w.r.t. the original continuous dictionary $\lbra{\m{a}\sbra{f}:\; f\in\bT}$, where $w\sbra{f}\geq 0$ is a weighting function. For $\m{Y}\in\bC^{N\times L}$, we define its weighted atomic norm w.r.t. $\cA^w$ as its atomic norm induced by $\cA^w$: According to the definition above, $w\sbra{f}$ specifies 