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On the convergence rate of an inexact proximal point algorithm for quasiconvex minimization on Hadamard manifolds

Nancy Baygorrea (nbaygorrea***at***gmail.com)
Erik Papa Quiroz (erikpapa***at***gmail.com)
Nelson Maculan (maculan***at***cos.ufrj.br)

Abstract: In this paper we present a rate of convergence analysis of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.

Keywords: Proximal point method, quasiconvex function, Hadamard manifolds, nonsmooth optimization, abstract subdifferential, convergence rate.

Category 1: Global Optimization


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Entry Submitted: 05/03/2015
Entry Accepted: 05/03/2015
Entry Last Modified: 05/07/2015

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