Essential stability in unified vector optimization

Abstract

The emphasis of the paper is to examine the essential stability of efficient solutions for semicontinuous vector optimization problems, subject to the perturbation of objective function and feasible set. We obtain sufficient conditions for existence and characterization of essential efficient solutions, essential sets and essential components, where the efficient solutions are governed by an arbitrary preference relation in a real normed linear space. Further, we establish the density of the set of stable vector optimization problems in the sense of Baire category. We also exhibit that essential stability is weaker than examining continuity aspects of solution sets.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable comments and suggestions which improved the original manuscript greatly.

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Correspondence to Shiva Kapoor.

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Kapoor, S., Lalitha, C.S. Essential stability in unified vector optimization. J Glob Optim (2021). https://doi.org/10.1007/s10898-021-00996-2

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Keywords

  • Vector optimization
  • Essential sets
  • Essential components
  • Continuity
  • Semicontinuity

Mathematics Subject Classification

  • 90C29
  • 90C31
  • 46N10
  • 49J45