Joint minimization with alternating Bregman proximity operators

Heinz H Bauschke , Patrick L Combettes (1) , Dominikus Noll (2)

1 NC State - North Carolina State University [Raleigh]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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. 2000 Mathematics Subject Classification: Primary 90C25; Secondary 49M05, 49M45, 65K05, 90C30.

Mots clés: Alternating minimization; alternating projections; Bregman distance; Bregman projection; left proximity operator; Moreau envelope; proximal point algorithm; prox operator; right proximity operator

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Heinz H Bauschke, Patrick L Combettes, Dominikus Noll. Joint minimization with alternating Bregman proximity operators. Pacific journal of optimization, 2006. ⟨hal-01868791⟩