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Title: Perturbed Proximal Point Algorithm with Nonquadratic Kernel
Authors: Brohe, M.
Tossings, P.
Keywords: Proximal Point Algorithm
Bregman Functions
Generalized Resolvent Operator
Variational Convergence
Issue Date: 2000
Publisher: Institute of Mathematics and Informatics
Citation: Serdica Mathematical Journal, Vol. 26, No 3, (2000), 177p-206p
Abstract: Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions by taking simultaneously into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm.
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 3

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