Fast primal-dual algorithm with Tikhonov regularization for a linear equality constrained convex optimization problem

We propose a fast primal-dual algorithm with Tikhonov regularization for solving a linear equality constrained convex optimization problem in a Hilbert space. When the Tikhonov regularization coefficient converges rapidly to zero, we prove that the proposed algorithm enjoys fast convergence rates for the objective function, the primal-dual gap and the feasibility violation, while when the Tikhonov regularization coefficient converges slowly to zero, we prove that the primal sequence generated by the algorithm converges strongly to the minimal norm solution of the problem. Finally, we perform some numerical experiments to illustrate the efficiency of our algorithm.