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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)

  • Jurandir de O. Lopes

    (Federal University of Piauí)

  • João Carlos de O. Souza

    (UFPI - Universidade Federal do Piauí, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

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," Post-Print hal-03866947, HAL.
    • Handle: RePEc:hal:journl:hal-03866947
    DOI: 10.1007/s10898-022-01240-1
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03866947
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