I have a problem in hand for which I need to compute the proximal operator of the composite function $ {\left\| \mbox{Hankel} (x) \right\|}_{\ast} $ where $ x \in \mathbb R^N $ and $ \left\| \cdot \right\|_{\ast} $ denotes the matrix nuclear norm.
For a general matrix $X$, the proximal map of the $\| X \|_{\ast}$ becomes a soft-thresholding of the singular values. I'll be grateful if somebody help me to evaluate the proximal map of $\| \mbox{Hankel} (x)\|_{\ast}$.