We address two well known iterative regularization methods for ill-posed problems (Landweber and iterated-Tikhonov methods) and discuss how to improve the performance of these classical methods by using convex analysis tools. The talk is based on two recent articles (2018): Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method (with R.Boiger, B.F.Svaiter), and On a family of gradient type projection methods for nonlinear ill-posed problems (with B.F.Svaiter)