Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea; Erik Alex Papa Quiroz; Nelson Maculan

doi:10.1007/s40305-016-0133-3

Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea
, Erik Alex Papa Quiroz
, Nelson Maculan

Universidade Federal do Rio de Janeiro

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory in economy.

Original language	English
Pages (from-to)	397-424
Number of pages	28
Journal	Journal of the Operations Research Society of China
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s40305-016-0133-3
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Abstract subdifferential
Hadamard manifolds
Nonsmooth optimization
Proximal point method
Quasiconvex function

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10.1007/s40305-016-0133-3

Cite this

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title = "Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds",

abstract = "In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory in economy.",

keywords = "Abstract subdifferential, Hadamard manifolds, Nonsmooth optimization, Proximal point method, Quasiconvex function",

author = "Nancy Baygorrea and \{Papa Quiroz\}, \{Erik Alex\} and Nelson Maculan",

note = "Publisher Copyright: {\textcopyright} 2016, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.",

year = "2016",

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T1 - Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

AU - Baygorrea, Nancy

AU - Papa Quiroz, Erik Alex

AU - Maculan, Nelson

PY - 2016/12/1

Y1 - 2016/12/1

N2 - In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory in economy.

AB - In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory in economy.

KW - Abstract subdifferential

KW - Hadamard manifolds

KW - Nonsmooth optimization

KW - Proximal point method

KW - Quasiconvex function

UR - https://www.scopus.com/pages/publications/84995595732

U2 - 10.1007/s40305-016-0133-3

DO - 10.1007/s40305-016-0133-3

M3 - Article

AN - SCOPUS:84995595732

SN - 2194-668X

VL - 4

SP - 397

EP - 424

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

IS - 4

ER -

Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

Abstract

Keywords

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