Joint minimization with alternating Bregman proximity operators

H. H. Bauschke (hbauschkuoguelph.ca)
P. L. Combettes (plcmath.jussieu.fr)
D. Noll (nollmip.ups-tlse.fr)

Abstract: A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of joint minimization problems. We provide a comprehensive convergence analysis of this algorithm. Our framework is shown to capture and extend various optimization methods.

Keywords: Alternating minimization, alternating projections, Bregman distance, Bregman projection, left proximity operator, Moreau envelope, proximal point algorithm, prox operator, right proximity operator.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

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Entry Submitted: 12/28/2004
Entry Accepted: 12/28/2004
Entry Last Modified: 12/28/2004

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