  We develop a novel algorithm for sparse Stokes parameters imaging in radio
interferometry under the polarization constraint. The latter is a physical
non-linear relation between the Stokes parameters, imposing that the
polarization intensity is a lower bound on the total intensity. To solve the
joint inverse Stokes imaging problem including this bound, we leverage
epigraphical projection techniques in convex optimization and design a
primal-dual method offering a highly flexible and parallelizable structure. In
addition, we propose to regularize each Stokes parameter map through an average
sparsity prior in the context of a reweighted analysis approach (SARA). The
resulting approach is dubbed Polarized SARA. We demonstrate on simulated
observations of M87 with the Event Horizon Telescope that imposing the
polarization constraint leads to superior image quality. The results also
confirm that the performance of the average sparsity prior surpasses the
alternative state-of-the-art priors for polarimetric imaging.
