On the relation between bundle methods for maximal monotone inclusions and hybrid proximal point algorithms
Mikhail Solodov | Sagastizabal, Claudia
budle methods | proximal point methods
We demonstrate that bundle methods for computing zeroes of general maximal monotone operators can be cast as a special case in a certain class of hybrid proximal point algorithms. This fact is significant for several reasons. First, it provides an alternative convergence proof, which is technically simple, for serious steps of bundle methods by invoking the corresponding results for hybrid proximal point methods. This includes the linear rate of convergence results, which were not available previously. Second, relating the two methodologies supplies a computationally realistic implementation of hybrid proximal point methods for the most general case, i.e., for operators without any particular structure.