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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 Two Proximal Point Algorithms with Possible Unbounded Error Sequences
Type
JournalPaper
Keywords
Maximal monotone operator · Proximal point algorithm · Resolvent operator · Metric projection · Hilbert space
Year
2017
Journal Journal of optimization theory and applications
DOI
Researchers Behzad Djafari Rouhani ، Sirous Moradi

Abstract

We consider a proximal point algorithmwith errors for a maximalmonotone operator in a real Hilbert space, previously studied by Boikanyo and Morosanu, where they assumed that the zero set of the operator is nonempty and the error sequence is bounded. In this paper, by using our own approach, we significantly improve the previous results by giving a necessary and sufficient condition for the zero set of the operator to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the zero set of the operator, without assuming the boundedness of the error sequence. We study also in a similar way the strong convergence of a new proximal point algorithm and present some applications of our results to optimization and variational inequalities.