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Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis

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Abstract

In this paper, we characterize different kinds of multiobjective robustness concepts via the well-known oriented distance function. By using characterizations of several set relations via the oriented distance function, together with the help of image space analysis, we construct some suitable subsets of the scalarization image space to obtain equivalent characterizations for various robust solutions for uncertain multiobjective optimization problems based on a set approach.

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Acknowledgements

Authors are grateful to the referees for their valuable suggestions and comments to improve the first draft of this paper. In this paper, Q. H. Ansari was supported by a research Grant of DST-SERB No. EMR/2016/005124.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari & Pradeep Kumar Sharma

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

  3. Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, 06099, Halle (Saale), Germany

    Elisabeth Köbis

Authors
  1. Qamrul Hasan Ansari
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  2. Elisabeth Köbis
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  3. Pradeep Kumar Sharma
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Correspondence to Qamrul Hasan Ansari.

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Communicated by Jafar Zafarani.

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Ansari, Q.H., Köbis, E. & Sharma, P.K. Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis. J Optim Theory Appl 181, 817–839 (2019). https://doi.org/10.1007/s10957-019-01505-y

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