Comments on “The Proximal Point Algorithm Revisited”



Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Brézis and Lions concerning the proximal point algorithm for monotone inclusion in an infinite-dimensional Hilbert space. One assumption is the algorithm’s strong convergence. In this paper, we derive a new upper bound on this decreasing positive sequence and thus achieve the same improvement without requiring this assumption.


Monotone inclusion Convex minimization Proximal point algorithm Rate of convergence 

Mathematics Subject Classification

58E35 65K15 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouPeople’s Republic of China

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