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Stability and Scalarization for a Unified Vector Optimization Problem

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Shiva Kapoor

  2. Department of Mathematics, University of Delhi South Campus, Benito Juarez Road, New Delhi, 110 021, India

    C. S. Lalitha

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  1. Shiva Kapoor
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  2. C. S. Lalitha
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Correspondence to Shiva Kapoor.

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Communicated by Marcin Studniarski.

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Kapoor, S., Lalitha, C.S. Stability and Scalarization for a Unified Vector Optimization Problem. J Optim Theory Appl 182, 1050–1067 (2019). https://doi.org/10.1007/s10957-019-01514-x

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