In the 1960s Lev Meerovich Bregman developed an optimization algorithm [1] which became rather popular beginning of 2000s. It’s not my intention to present the proofs for all the algorithmic finesse, but rather the general ideas why it is so appealing. Some ramifications and new algorithms, that were derived from the original Bregman algorithm (e.g. [2, 3, 4]), will be presented in subsequent posts.
Finding a common point in a set of convex sets Let’s assume we are given a family of convex sets $A_i$, with $i=1, \ldots, n$.