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A proximal point algorithm converging strongly for general errors. (English) Zbl 1202.90271
Summary: A proximal point algorithm (PPA) for maximal monotone operators with appropriate regularization parameters is considered. A strong convergence result for the PPA is stated and proved under the general condition that the error sequence tends to zero in norm. Note that {\it R. T. Rockafellar} [SIAM J. Control Optimization 14, 877--898 (1976; Zbl 0358.90053)] assumed summability for the error sequence to derive weak convergence of the PPA in its initial form, and this restrictive condition on the errors has been extensively used so far for different versions of the PPA. Thus, this Note provides a solution to a long standing open problem and in particular offers new possibilities towards the approximation of the minimum points of convex functionals.

90C48Programming in abstract spaces
90C56Derivative-free methods; methods using generalized derivatives
Full Text: DOI
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