TY - JOUR
A2 - Jebelean, Petru
AU - Verma, Ram U.
PY - 2009
DA - 2009/11/22
TI - Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis
SP - 691952
VL - 2009
AB - Based on a notion of relatively maximal (m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.
SN - 0161-1712
UR - https://doi.org/10.1155/2009/691952
DO - 10.1155/2009/691952
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi Publishing Corporation
KW -
ER -