On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea, Erik Alex Papa Quiroz, Nelson Maculan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper, we present an analysis about the rate of convergence 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.

Original languageEnglish
Pages (from-to)457-467
Number of pages11
JournalJournal of the Operations Research Society of China
Volume5
Issue number4
DOIs
StatePublished - 1 Dec 2017
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro (UFRJ), Brazil.

Keywords

  • Abstract subdifferential
  • Convergence rate
  • Hadamard manifolds
  • Nonsmooth optimization
  • Proximal point method
  • Quasiconvex function

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