Volume 10, Number 3, December 2009, pp. 471-485
Simeon Reich and Shoham Sabach
Key words:
Banach space, Bregman projection, Legendre function, maximal monotone operator, monotone operator, proximal point algorithm, resolvent, totally convex function.
Mathematices Subject Classification: Primary 47H05; Secondary 47J25.
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We establish a strong convergence theorem for a proximal-type algorithm which approximates (common) zeroes of maximal monotone operators in reflexive Banach spaces. This algorithm employs a well-chosen convex function. The behavior of the algorithm in the presence of computational errors and in the case of zero free operators is also analyzed. Finally, we mention several corollaries, variations and applications.
A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces