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Two Models in Optimization and Control

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Abstract

The phase space of a controllable system was considered as the space of indices partially ordered by the domination cone. It was shown in what way the cone varies with increasing number of indices or interacting systems. Approaches to constructing on the domination cone of a metric enabling numerical evaluation of the cone elements were analyzed.

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REFERENCES

  1. Kholevo, A.S., Veroyatnostnye i statisticheskie aspekty kvantovoi teorii (Probabilistic and Statistical Aspects of the Quantum Theory), Moscow: Nauka, 1980.

    Google Scholar 

  2. Dubrovin, B.A., Novikov, S.P., and Fomenko, A.T., Sovremennaya geometriya (Modern Geometry), Moscow: Nauka, 1986.

    Google Scholar 

  3. Farrel, M.J., The Measurement of Productive Efficiency, J. Royal Statist. Soc., Series A (general), 1957, part III, pp. 253-281.

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

    Google Scholar 

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

    Google Scholar 

  6. Makarov, V.L. and Rubinov, A.M., Matematicheskaya teoriya ekonomicheskoi dinamiki i ravnovesiya (Mathematical Theory of Economic Dynamics and Equilibrium), Moscow: Nauka, 1973.

    Google Scholar 

  7. Propoi, A.I., Principle of Equivalence in Control of Motion. I, Avtom. Telemekh., 1999, no. 10, pp. 89-96.

    Google Scholar 

  8. Propoi, A.I., Principle of Equivalence in Control of Motion. II, Avtom. Telemekh., 1999, no. 12, pp. 57-66.

    Google Scholar 

  9. 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 

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

    Google Scholar 

  11. Propoi, A.I., Problems of Optimization and Learning for Nonlocal Search in Excitable Media. I, Avtom. Telemekh., 1999, no. 1, pp. 57-66.

    Google Scholar 

  12. Rockafellar, R.T., Convex Analysis, Princeton: Princeton Univ. Press, 1970. Translated under the title Vypuklyi analiz, Moscow: Mir, 1973.

    Google Scholar 

  13. Weyl, H., Raum, Zeit, Materie, Berlin: Springer, 1923.

    Google Scholar 

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  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. Two Models in Optimization and Control. Automation and Remote Control 65, 19–29 (2004). https://doi.org/10.1023/B:AURC.0000011687.30046.31

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  • DOI: https://doi.org/10.1023/B:AURC.0000011687.30046.31

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