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

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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.

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Acknowledgements

We would like to thank the referees for their constructive remarks which allow us to improve our work. J.C.O. Souza was supported in part by CNPq Grants 424169/2018-5 and 313901/2020-1. The project leading to this publication has received funding from the French government under the “France 2030” investment plan managed by the French National Research Agency (reference: ANR-17-EURE-0020) and from Excellence Initiative of Aix-Marseille University - A*MIDEX.

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Authors and Affiliations

  1. CSHNB, Federal University of Piauí, Picos, PI, 64607-670, Brazil

    João S. Andrade

  2. Department of Mathematics, CCN, Federal University of Piauí, Teresina, PI, 64049-550, Brazil

    João S. Andrade, Jurandir de O. Lopes & João Carlos de O. Souza

  3. Aix Marseille University, CNRS, AMSE, Marseille, France

    João Carlos de O. Souza

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  1. João S. Andrade
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  2. Jurandir de O. Lopes
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  3. João Carlos de O. Souza
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Correspondence to João Carlos de O. Souza.

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Andrade, J.S., Lopes, J.d.O. & Souza, J.C.d.O. An inertial proximal point method for difference of maximal monotone vector fields in Hadamard manifolds. J Glob Optim 85, 941–968 (2023). https://doi.org/10.1007/s10898-022-01240-1

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  • DOI: https://doi.org/10.1007/s10898-022-01240-1

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