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.
| Original language | English |
|---|---|
| Pages (from-to) | 481-503 |
| Number of pages | 23 |
| Journal | Taiwanese Journal of Mathematics |
| Volume | 19 |
| Issue number | 2 |
| DOIs | |
| State | Published - 22 Mar 2015 |
Bibliographical note
Publisher Copyright:© 2015, Mathematical Society of the Rep. of China. All rights reserved.
Keywords
- Accretive operator
- Maximal monotone operator
- Metric projection mapping
- Proximal point algorithm
- Regularization method
- Resolvent identity
- Strong convergence
- Uniformly Gâteaux differentiable norm
ASJC Scopus subject areas
- General Mathematics
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