One possible way of solving a constrained optimization problem consists in its transformation into a sequence of unconstrained problems. In this paper is presented the connection between three of this methods; namely the method of centers (Huard), the SUMT (sequential unconstrained minimization technique) without parameters (Fiacco and Mccormick) and the method of barycenters (Lommatzsch). For the metyhod of centers is presented a simple proof of convergence without convexity assumptions, developed from an idea of Huard Further are given relations between some regularity conditions, which were used for this methods.