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A unified minimal solution in set optimization

  • KhushbooEmail author
  • C. S. Lalitha
Article
  • 65 Downloads

Abstract

In this paper we extend the notion of minimal solutions for a vector optimization problem considered by Flores-Bazán et al. (J Optim Theory Appl 164:455–478, 2015) to a set-valued optimization problem, with both vector and set solution criteria. Also, we extend the Gerstewitz function proposed by Hernández and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) and use it to scalarize minimal solutions with respect to set criterion. We also provide an existence result of minimal solutions with set criterion. Finally, we investigate links between the minimal solutions with respect to vector criterion and set criterion.

Keywords

Set-valued optimization Nonlinear scalarization Generalized Gerstewitz’s function 

Mathematics Subject Classification

54C60 90C26 90C29 90C31 

Notes

Acknowledgements

The authors wish to thank referee and associate editor for their suggestions which helped to improve the presentation of this article. This research, for the second author, was supported by MATRIC scheme of Department of Science and Technology, India.

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia
  2. 2.Department of MathematicsUniversity of Delhi South CampusNew DelhiIndia

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