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Stability for Properly Quasiconvex Vector Optimization Problem

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Abstract

The aim of this paper is to study the stability aspects of various types of solution set of a vector optimization problem both in the given space and in its image space by perturbing the objective function and the feasible set. The Kuratowski–Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set of the original problem is established assuming the objective functions to be (strictly) properly quasi cone-convex.

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Acknowledgements

Research of C.S. Lalitha was supported by R&D Doctoral Research Programme funds for university faculty.

The authors are grateful to the reviewers and the associate editor for their valuable comments and suggestions which helped in improving the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi South Campus, Benito Jaurez Road, New Delhi, 110021, India

    C. S. Lalitha

  2. Department of Mathematics, St. Stephen’s College, University of Delhi, Delhi, 110007, India

    Prashanto Chatterjee

Authors
  1. C. S. Lalitha
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  2. Prashanto Chatterjee
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Corresponding author

Correspondence to Prashanto Chatterjee.

Additional information

Communicated by Marcin Studniarski.

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Lalitha, C.S., Chatterjee, P. Stability for Properly Quasiconvex Vector Optimization Problem. J Optim Theory Appl 155, 492–506 (2012). https://doi.org/10.1007/s10957-012-0079-5

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  • DOI: https://doi.org/10.1007/s10957-012-0079-5

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