Comments on “The Proximal Point Algorithm Revisited”
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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.
KeywordsMonotone inclusion Convex minimization Proximal point algorithm Rate of convergence
Mathematics Subject Classification58E35 65K15