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Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems

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Abstract

The paper describes new results in the field of multiobjective optimization techniques. The Interactive Decision Maps (IDM) technique is based on approximation of Feasible Criterion Set (FCS) and subsequent visualization of the Pareto frontier of FCS by interactive displaying the bi-criteria slices of FCS. The Estimation Refinement (ER) method is now the main method for approximating convex FCS in the framework of IDM. The properties of the ER method are studied. We prove that the number of facets of the approximation constructed by ER and the number of the support function calculations of an approximated set are asymptotically optimal. These results are important from the point of view of real-life applications of ER.

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Authors and Affiliations

  1. Rey Juan Carlos University, c\ Tulipán s/n., 28933, Móstoles, Spain

    Roman V. Efremov

  2. Dorodnicyn Computing Centre of the Russian Academy of Sciences, Vavilov st. 40, 119333, Moscow, Russia

    Georgy K. Kamenev

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  1. Roman V. Efremov
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  2. Georgy K. Kamenev
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Correspondence to Roman V. Efremov.

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Efremov, R.V., Kamenev, G.K. Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems. Ann Oper Res 166, 271–279 (2009). https://doi.org/10.1007/s10479-008-0418-y

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  • DOI: https://doi.org/10.1007/s10479-008-0418-y

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