In this article we study the hybrid extragradient method coupled with approximation and penalty schemes for convex minimization problems. Under certain hypotheses, which include, for example, the case of Tikhonov regularization, we prove asymptotic convergence of the method to the solution set of our minimization problem. When we use schemes of penalization or barrier, we can show asymptotic convergence using the well-known fast/slow parameterization techniques and exploiting the existence and finite length of an optimal path.
Bibliographical noteFunding Information:
The author thanks Felipe Alvarez from Universidad de Chile and Lionel Thibault from Université de Montpellier 2, France, for useful discussions on this subjects. The author was partially supported by FONDECYT grant no. 11090328.
- convex optimization
- global convergence
- hybrid method
- parametric approximation
- proximal point