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ON THE CONVERGENCE OF INEXACT PROXIMAL POINT ALGORITHM ON HADAMARD MANIFOLDS

P. Ahmadi and H. Khatibzadeh
Taiwanese Journal of Mathematics
Vol. 18, No. 2 (April 2014), pp. 419-433
Stable URL: http://www.jstor.org/stable/taiwjmath.18.2.419
Page Count: 15
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ON THE CONVERGENCE OF INEXACT PROXIMAL POINT ALGORITHM ON HADAMARD MANIFOLDS
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Abstract

Abstract 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. 2010 Mathematics Subject Classification: 47H05, 49J40. Key words and phrases: Proximal point algorithm, Maximal monotone operator, Resolvent, Subdifferential, Convergence, Hadamard manifold.

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