Geodesic
Perturbed Proximal Point Algorithm with Nonquadratic Kernel
Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 177-206.

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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.
Keywords: Proximal Point Algorithm, Bregman Functions, Generalized Resolvent Operator, Variational Convergence 
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     author = {Brohe, M. and Tossings, P.},
     title = {Perturbed {Proximal} {Point} {Algorithm} with {Nonquadratic} {Kernel}},
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Brohe, M.; Tossings, P. Perturbed Proximal Point Algorithm with Nonquadratic Kernel. Serdica Mathematical Journal, Tome 26 (2000) no. 3, pp. 177-206. http://geodesic.mathdoc.fr/item/SMJ2_2000_26_3_a0/