  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.
