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An inertial proximal point method for difference of maximal monotone vector fields in Hadamard manifolds

Author

Listed:
  • João S. Andrade

    (Federal University of Piauí
    Federal University of Piauí)

  • Jurandir de O. Lopes

    (Federal University of Piauí)

  • João Carlos de O. Souza

    (Federal University of Piauí
    Aix Marseille University, CNRS, AMSE)

Abstract

We propose an inertial proximal point method for variational inclusion involving difference of two maximal monotone vector fields in Hadamard manifolds. We prove that if the sequence generated by the method is bounded, then every cluster point is a solution of the non-monotone variational inclusion. Some sufficient conditions for boundedness and full convergence of the sequence are presented. The efficiency of the method is verified by numerical experiments comparing its performance with classical versions of the method for monotone and non-monotone problems.

Suggested Citation

  • João S. Andrade & Jurandir de O. Lopes & João Carlos de O. Souza, 2023. "An inertial proximal point method for difference of maximal monotone vector fields in Hadamard manifolds," Journal of Global Optimization, Springer, vol. 85(4), pages 941-968, April.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01240-1
    DOI: 10.1007/s10898-022-01240-1
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    References listed on IDEAS

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    1. J. Souza & P. Oliveira, 2015. "A proximal point algorithm for DC fuctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 63(4), pages 797-810, December.
    2. M. Alimohammady & M. Ramazannejad, 2016. "Inertial proximal algorithm for difference of two maximal monotone operators," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 1-8, March.
    3. NESTEROV , Yu. & TODD, Mike, 2002. "On the Riemannian geometry defined by self-concordant barriers and interior-point methods," LIDAM Reprints CORE 1595, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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