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A Steepest Descent-Like Method for Variable Order Vector Optimization Problems

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Abstract

In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case.

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Acknowledgements

The authors would like to thank the anonymous referees, whose suggestions helped us to improve the presentation of this paper. We also very grateful to Prof. Dr. Ole Peter Smith for correcting the manuscript.

This research was supported by Project CAPES-MES-CUBA 226/2012 “Modelos de Otimização e Aplicações”. First author was partially supported by PROCAD-nf-UFG/UnB/IMPA research and PRONEX-CNPq-FAPERJ Optimization research.

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Authors and Affiliations

  1. Universidade Federal de Goiás, Goiânia, Brazil

    J. Y. Bello Cruz

  2. Facultad de Matemática y Computación, Universidad de La Habana, Havana, Cuba

    G. Bouza Allende

Authors
  1. J. Y. Bello Cruz
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  2. G. Bouza Allende
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Correspondence to G. Bouza Allende.

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Bello Cruz, J.Y., Bouza Allende, G. A Steepest Descent-Like Method for Variable Order Vector Optimization Problems. J Optim Theory Appl 162, 371–391 (2014). https://doi.org/10.1007/s10957-013-0308-6

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  • DOI: https://doi.org/10.1007/s10957-013-0308-6

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