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Approximation of a Metric on a Dominating Cone

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Abstract

A theorem on the representation of a pseudoball of a dominating cone is proven. This theorem is an analog of the Caratheodory theorem on the representation of convex sets. The theorem allows to develop numerical methods for quantitative evaluation of systems in many indicators.

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REFERENCES

  1. Propoi, A.I., On Construction of a Pseudometric on a Dominating Cone. I, Avtom. Telemekh., 2004, no. 4, pp. 81–91.

    Google Scholar 

  2. Propoi, A.I., On Construction of a Pseudometric on a Dominating Cone. II, Avtom. Telemekh., 2004, no. 5, pp. 52–61.

    Google Scholar 

  3. Yu, P.L., Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, JOTA, 1974, vol. 14, no. 3, pp. 319–377.

    Google Scholar 

  4. Kostrikin, A.I. and Manin, Yu.I., Lineinaya algebra i geometriya(Linear Algebra and Geometry), Moscow: Nauka, 1986.

    Google Scholar 

  5. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal'nykh zadach(The Theory of Extremal Problems), Moscow: Nauka, 1974.

    Google Scholar 

  6. Charnes, A., Cooper, W.W., and Rhodes, E., Measuring the Efficiency of Decision Making Units, EJOR, 1978, no. 2, pp. 429–444.

    Google Scholar 

  7. Banker, R.D., Charnes, A., and Cooper, W.W., Some Models for Estimating Technical and Scale Inef-ficiences in date envelopment analysis, Manag. Sci., 1984, vol. 30, no. 9. pp. 1078–1092.

    Google Scholar 

  8. Seiford, L.M. and Thrall, R.M., Recent Developments in DEA. The Mathematical Programming Approach to Frontier Analysis, J. Econometrics, 1990, vol. 46, no. 1, pp. 7–38.

    Google Scholar 

  9. Shephard, R.W., Theory of Cost and Production Functions, Princeton: Princeton Univ. Press, 1970.

    Google Scholar 

  10. Krasnosel'skii M.A., Polozhitel'nye resheniya operatornykh uravnenii(Positive Solutions of Operators Equations), Moscow: Nauka, 1962.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    A. I. Propoi

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  1. A. I. Propoi
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Propoi, A.I. Approximation of a Metric on a Dominating Cone. Automation and Remote Control 65, 1231–1239 (2004). https://doi.org/10.1023/B:AURC.0000038725.83948.ed

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  • DOI: https://doi.org/10.1023/B:AURC.0000038725.83948.ed

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