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

doi:10.1007/s40305-016-0129-z

Journal of the Operations Research Society of China ›› 2017, Vol. 5 ›› Issue (4): 457-467.doi: 10.1007/s40305-016-0129-z

Special Issue: Continuous Optimization

• Continuous Optimization • Previous Articles Next Articles

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

Nancy Baygorrea¹ · Erik Alex Papa Quiroz¹ ·Nelson Maculan¹

1 Federal University of Rio de Janeiro, PESC-COPPE-UFRJ, PO Box 68511,Rio de Janeiro CEP 21941-972, Brazil

Online:2017-12-30 Published:2017-12-30
Supported by:
This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro (UFRJ), Brazil.

Abstract

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.

Key words: Proximal point method ·, Quasiconvex function ·, Hadamard manifolds ·Nonsmooth optimization ·, Abstract subdifferential ·, Convergence rate

Nancy Baygorrea, Erik Alex Papa Quiroz, Nelson Maculan. On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds[J]. Journal of the Operations Research Society of China, 2017, 5(4): 457-467.

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

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