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An inexact proximal point method for variational inequality on Hadamard manifolds

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G. C. Bento, O. P. Ferreira, E. A. Papa Quiroz

Optimization and Control · Submitted 3 Mar 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties.

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arXiv ID2103.02116 (version 1)
Pith IDJKPBK63B, Pith's permanent record of this paper and its review
CitationE. A. Papa Quiroz, G. C. Bento, O. P. Ferreira. "An inexact proximal point method for variational inequality on Hadamard manifolds." arXiv:2103.02116 (2021). https://pith.science/paper/JKPBK63B
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arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is approximated by using the enlargement of the vector field in consideration and then the next iterated is obtained by solving this subproblem allowing a suitable error tolerance. As an application, we obtain an inexact proximal point method for constrained optimization problems, equilibrium problems and nonlinear optimization problems on Hadamard manifolds.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. contribution 1.00 0.93 0.23 asserted 1.00
s1 The proposed algorithm is inexact in two sense. method 0.76 0.82 0.04 asserted 1.00
s2 First, each proximal subproblem is approximated by using the enlargement of the vector field in consideration and then the next iterated is obtained by solving this subproblem allowing a suitable error tolerance. method 1.00 0.88 0.06 asserted 1.00
s3 As an application, we obtain an inexact proximal point method for constrained optimization problems, equilibrium problems and nonlinear optimization problems on Hadamard manifolds. contribution 0.75 0.93 0.16 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is approximated by using the enlargement of the vector field in consideration and then the next iterated is obtained by solving this subproblem allowing a suitable error tolerance. As an application, we obtain an inexact proximal point method for constrained optimization problems, equilibrium problems and nonlinear optimization problems on Hadamard manifolds.

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