GENERALIZED PROXIMAL POINT ALGORITHM FOR CONVEX-OPTIMIZATION

Ha (Ref. 1) recently introduced a generalized proximal point algorithm for solving a generalized equation. In this note, we present a genera lized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that, instead of addin g a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria for approximate soluti ons given by Rockafellar (Ref. 2) and Auslender (Ref. 3) and present c onvergence results. Finally, we show how this algorithm can be applied to solve block-angular linear and quadratic programming problems.