A fast algorithm for smooth convex minimization problems and its application to inverse source problems

In this paper, we propose a fast algorithm for smooth convex minimization problems in a real Hilbert space whose objective functionals have Lipschitz continuous Fréchet derivatives. The main advantage of the proposed algorithm is that it has the optimal-order convergence rate and faster than Nesterov’s algorithm with the best setting. To demonstrate the efficiency of the proposed algorithm, we compare it with Nesterov’s algorithm in several examples, including inverse source problems for elliptic and hyperbolic PDEs. The numerical tests show that the proposed algorithm converges faster than Nesterov’s algorithm.