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Stability and Scalarization for a Unified Vector Optimization Problem

  • Shiva KapoorEmail author
  • C. S. Lalitha
Article
  • 53 Downloads

Abstract

This paper aims at investigating the Painlevé–Kuratowski convergence of solution sets of a sequence of perturbed vector problems, obtained by perturbing the feasible set and the objective function of a unified vector optimization problem, in real normed linear spaces. We establish convergence results, both in the image and given spaces, under the assumptions of domination and strict domination properties. Moreover, scalarization techniques are employed to establish the Painlevé–Kuratowski convergence in terms of the solution sets of a sequence of scalarized problems.

Keywords

Painlevé–Kuratowski convergence Vector optimization Gamma-convergence Domination property Scalarization 

Mathematics Subject Classification

90C29 90C31 90C26 

Notes

Acknowledgements

The research of first author is supported by CSIR-UGC, Junior Research Fellowship, India, National R & D Organisation (Ref. No: 22/12/2013(ii)EU-V). The authors are grateful to Prof. Marcin Studniarski and the reviewers for their valuable comments and suggestions, which helped in improving the paper. Further, authors are thankful to one of the reviewers for pointing out the fact that Theorem 4.3 holds, if D is assumed to be a convex cone.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

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

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