Ha [Ha90] recently introduced a generalized proximal point algorithm for solving a generalized equation. In this note, we present a generalized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that, instead of adding a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria for approximate solutions given by Rockafellar [Roc76b] and Auslender [Aus87] and present convergence results. Finally, we show how this algorithm can be applied to solve block-angular linear and quadratic programming problems.

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