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We investigate the strong convergence properties of a Nesterov type algorithmwith two Tikhonov regularization terms in connection to the minimizationproblem of a smooth convex function $f.$ We show that the generated sequencesconverge strongly to the minimal norm element from $\argmin f$. We also showthat from a practical point of view the Tikhonov regularization does not affectNesterov's optimal convergence rate of order $\mathcal{O}(n^{-2})$ for thepotential energies $f(x_n)-\min f$ and $f(y_n)-\min f$, where $(x_n),\,(y_n)$are the sequences generated by our algorithm. Further, we obtain fastconvergence to zero of the discrete velocity, but also some estimatesconcerning the value of the gradient of the objective function in the generatedsequences.

A Nesterov type algorithm with double Tikhonov regularization: fast  convergence of the function values and strong convergence to the minimal norm  solution