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A Newton-Like Method for Variable Order Vector Optimization Problems

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Abstract

A Newton approach is proposed for solving variable order smooth constrained vector optimization problems. The concept of strong convexity is presented, and its properties are analyzed. It is thus obtained that the Newton direction is well defined and that the algorithm converges. Moreover, the rate of convergence is obtained under ordering structures satisfying a mild hypothesis.

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Acknowledgements

The first author was partially supported by CNPq Grants 458479/2014-4 and 3122077/2014-9, the second author was partially supported by CAPES/FAPEG 10/2013 and 08/2014, and the third author was partially supported by CAPES, CAPES/MES/Cuba Project 226/2012 Optimization and Applications. The second author was also partially supported by Alexander von Humboldt Foundation during his stay at Martin Luther University, where part of this research was carried out.

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Authors and Affiliations

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

    Glaydston de Carvalho Bento

  2. Faculty of Mathematics and Computer Science, University of Habana, Habana, 10400, Cuba

    Gemayqzel Bouza Allende

  3. DM, Universidade Federal do Piauí, Teresina, Brazil

    Yuri Rafael Leite Pereira

Authors
  1. Glaydston de Carvalho Bento
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  2. Gemayqzel Bouza Allende
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  3. Yuri Rafael Leite Pereira
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Correspondence to Yuri Rafael Leite Pereira.

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de Carvalho Bento, G., Bouza Allende, G. & Pereira, Y.R.L. A Newton-Like Method for Variable Order Vector Optimization Problems. J Optim Theory Appl 177, 201–221 (2018). https://doi.org/10.1007/s10957-018-1236-2

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  • DOI: https://doi.org/10.1007/s10957-018-1236-2

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