Efficient primal-dual fixed point algorithm with dynamic stepsize for   convex problems with applications to imaging restoration
  We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We design a primal-dual fixed point algorithm with dynamic stepsize based on the proximity operator and obtain a scheme with a closed form solution for each iteration. Based on Modified Mann iteration and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithm. 
Meng Wen, Shigang Yue, Yuchao Tang, Jigen Peng
math.OC