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Sequential characterization of statistical epi-convergence

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Abstract

Epi-convergence is used as an efficient tool in optimization theory. It finds optimal solutions in such a way that it ensures the convergence of infimum values. In some cases, some functions may not conform to an expected pattern and reduce the efficiency of optimization. Moreover, obtaining epi-limit function may fail due to disruption of these functions. For that reason, it may be necessary to use an alternative method that diminishes the effect of such functions by excluding them from consideration. In this paper, we give a sequential characterization of statistical epi-convergence which enables us to eliminate corrupted functions deviate from the majority of the data. Therefore, statistical epi-limit inferior and superior are defined. Then, we show that sequential characterization of statistical epi-convergence is not biconditional as its ordinary definition. At the end, these definitions lead the way through the conditions for statistical convergence of infimum values which is an essential property to solve optimization problems.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Art and Sciences, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey

    Şükrü Tortop & Yurdal Sever

  2. Yenimahalle, Yunusemre, Manisa, Turkey

    Özer Talo

Authors
  1. Şükrü Tortop
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  2. Yurdal Sever
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  3. Özer Talo
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Correspondence to Şükrü Tortop.

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Tortop, Ş., Sever, Y. & Talo, Ö. Sequential characterization of statistical epi-convergence. Soft Comput 24, 18565–18571 (2020). https://doi.org/10.1007/s00500-020-05092-3

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