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| Volume 2, Number 3, September 2006, pp. 401-424 | ||||||||
| Heinz H. Bauschke, Patrick L. Combettes and Dominikus Noll | ||||||||
| Key words: | ||||||||
| Alternating minimization, alternating projections, Bregman distance, Bregman projection, left proximity operator, Moreau envelope, proximal point algorithm, prox operator, right proximity operator | ||||||||
| Mathematices Subject Classification: 90C25, 49M05, 49M45, 65K05, 90C30 | ||||||||
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| 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. | |||
| Joint minimization with alternating Bregman proximity operators | ||