Preprint A82/2001
On the relation between bundle methods for maximal monotone inclusions and hybrid proximal point algorithms

Mikhail Solodov | Sagastizabal, Claudia

**Keywords: **
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.