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Characterization of Norm-Based Robust Solutions in Vector Optimization

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Abstract

In this paper, we study the norm-based robust (efficient) solutions of a vector optimization problem. We define two kinds of non-ascent directions in terms of Clarke’s generalized gradient and characterize norm-based robustness by means of the newly defined directions. This is done under a basic constraint qualification. We extend the provided characterization to vector optimization problems with conic constraints and semi-infinite ones. Moreover, we derive a necessary condition for norm-based robustness utilizing a non-smooth gap function.

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Acknowledgements

The authors would like to express their gratitude to the editor in chief of JOTA, handling editor, and two anonymous referees for their helpful comments on the earlier versions of the paper. The research was in part supported by a Grant from the Iran National Science Foundation (INSF) (No. 96005247).

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Morteza Rahimi & Majid Soleimani-damaneh

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  1. Morteza Rahimi
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  2. Majid Soleimani-damaneh
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Correspondence to Majid Soleimani-damaneh.

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Communicated by Fabián Flores-Bazán.

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Rahimi, M., Soleimani-damaneh, M. Characterization of Norm-Based Robust Solutions in Vector Optimization. J Optim Theory Appl 185, 554–573 (2020). https://doi.org/10.1007/s10957-020-01662-5

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