Open AccessON THE CONVERGENCE OF INEXACT PROXIMAL POINT ALGORITHM ON HADAMARD MANIFOLDS
Author(s) -
P. Ahmadi,
Hadi Khatibzadeh
Publication year - 2014
Publication title -
taiwanese journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.529
H-Index - 46
eISSN - 2224-6851
pISSN - 1027-5487
DOI - 10.11650/tjm.18.2014.3066
Subject(s) - mathematics , hadamard transform , hadamard three lines theorem , sequence (biology) , convergence (economics) , manifold (fluid mechanics) , singularity , monotone polygon , point (geometry) , algorithm , pure mathematics , hadamard matrix , mathematical analysis , geometry , mechanical engineering , biology , engineering , economics , genetics , economic growth
In this paper we consider the proximal point algorithm to approximate a singularity of a multivalued monotone vector field on a Hadamard manifold. We study the convergence of the sequence generated by an inexact form of the algorithm. Our results extend the results of [3, 25] to Hadamard manifolds as well as the main result of [11] with more general assumptions on the control sequence. We also give some application to optimization.
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