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Bregman Distan es Stephen Della Pietra, Vin ent Della Pietra, and John La erty O tober 8, 2001 CMU-CS-01-109 S hool of Computer S ien e Carnegie Mellon University Pittsburgh, PA 15213 Abstra t We formulate and prove a onvex duality theorem for Bregman distan es and present a te hnique based on auxiliary fun tions for deriving and proving onvergen e of iterative algorithms to minimize Bregman distan e subje t to linear onstraints.