In this paper we study the hybrid extragradient method coupled with approximation and penalty schemes for minimization problems. Under certain hypotheses, that include for example the case of Tikhonov regularization, we prove convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier we can show convergence using the so called slow/fast parametrization hypothesis and exploiting the existence and finite length of the central path. Assuming only finite length of the central path we can prove the convergence of the scheme to a solution of the constrained minimization problem when the functions belong to a special class of functions.
DIM-CMM N: CMM-B-07/07-185, Universidad de Chile, Jul/2007