A nested primal–dual FISTA-like scheme for composite convex optimization problems

We propose a nested primal–dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. The proposed algorithm can be interpreted as an inexact inertial forward–backward algorithm equipped with a prefixed number of inner primal–dual iterations for the proximal evaluation and a “warm–start” … Read more