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Sirous Moradi

Academic rank: Assistant Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Arak University
Address: Arak University
Phone:

Research

Title
Strong Convergence of Regularized New Proximal Point Algorithms
Type
JournalPaper
Keywords
47J25 · 47H05 · 47H09 · 90C29 · 90C90
Year
2019
Journal Journal of optimization theory and applications
DOI
Researchers Behzad Djafari Rouhani ، Sirous Moradi

Abstract

We consider the regularization of two proximal point algorithms (PPA)with errors for a maximalmonotone operator in a real Hilbert space, previously studied, respectively, by Xu, and by Boikanyo and Morosanu, where they assumed the zero set of the operator to be nonempty. We provide a counterexample showing an error in Xu’s theorem, and then we prove its correct extended version by giving a necessary and sufficient condition for the zero set of the operator to be nonempty and showing the strong convergence of the regularized scheme to a zero of the operator. This will give a first affirmative answer to the open question raised by Boikanyo and Morosanu concerning the design of a PPA, where the error sequence tends to zero and a parameter sequence remains bounded. Then, we investigate the second PPA with various new conditions on the parameter sequences and prove similar theorems as above, providing also a second affirmative answer to the open question of Boikanyo and Morosanu. Finally, we present some applications of our new convergence results to optimization and variational inequalities.