Abstract
It is known, by Rockafellar [SIAM J. Control Optim., 14 (1976), 877-898], that the proximal point algorithm (PPA) converges weakly to a zero of a maximal monotone operator in a Hilbert space, but it fails to converge strongly. Lehdili and Moudafi [Optimization, 37(1996), 239-252] introduced the new prox-Tikhonov regularization method for PPA to generate a strongly convergent sequence and established a convergence property for it by using the technique of variational distance in the same space setting. In this paper, the prox-Tikhonov regularization method for the proximal point algorithm of finding a zero for an accretive operator in the framework of Banach space is proposed. Conditions which guarantee the strong convergence of this algorithm to a particular element of the solution set is provided. An inexact variant of this method with non-summable error sequence is also discussed.
Citation
D. R. Sahu. Q. H. Ansari. J. C. Yao. "THE PROX-TIKHONOV-LIKE FORWARD-BACKWARD METHOD AND APPLICATIONS." Taiwanese J. Math. 19 (2) 481 - 503, 2015. https://doi.org/10.11650/tjm.19.2015.4972
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