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A Strongly Convergent Proximal Point Method for Vector Optimization

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Abstract

In this paper, we propose and analyze a variant of the proximal point method for obtaining weakly efficient solutions of convex vector optimization problems in real Hilbert spaces, with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. The proposed method is a hybrid scheme that combines proximal point type iterations and projections onto some special halfspaces in order to achieve the strong convergence to a weakly efficient solution. To the best of our knowledge, this is the first time that proximal point type method with strong convergence has been considered in the literature for solving vector/multiobjective optimization problems in infinite dimensional Hilbert spaces.

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Acknowledgements

We would like to thank the anonymous referees for their valuable suggestions and remarks that allowed us to improve the first draft of the paper. The work of the second author is supported in part by FAPEG/CNPq/PRONEM-201710267000532 and CNPq-312559/2019-4. Data sharing not applicable to this article as no datasets were generated or analyzed during the current study

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Authors and Affiliations

  1. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil

    Alfredo N. Iusem

  2. IME, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Brazil

    Jefferson G. Melo & Ray G. Serra

Authors
  1. Alfredo N. Iusem
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  2. Jefferson G. Melo
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  3. Ray G. Serra
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Correspondence to Jefferson G. Melo.

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Communicated by Guang-ya Chen.

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Iusem, A.N., Melo, J.G. & Serra, R.G. A Strongly Convergent Proximal Point Method for Vector Optimization. J Optim Theory Appl 190, 183–200 (2021). https://doi.org/10.1007/s10957-021-01877-0

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  • DOI: https://doi.org/10.1007/s10957-021-01877-0

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