Does CVX solve this prob. directly?

Does CVX solve this prob. directly?

max Re( conj©*y )
c
subject to ||conj(F) * c|| (infinity norm) <= 1

(This problem is
Dual prob. of

min ||x|| (Atomic norm)
x
subject to y = F*x)

Directly? (Without transforming this to SDP formulation)

Thanks.