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Analysis of Matrix-Convex Functions

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Abstract

The properties of matrix-convex functions, which may take values from an expanded numerical axis, are analyzed. Matrix convexity is specified by a pair of matrices, a final set of matrices, or an infinite family of matrices. The results obtained are used in the theory of differential games.

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REFERENCES

  1. B. N. Pshenichnyi and V. V. Ostapenko, Differential Games [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  2. V. V. Ostapenko and L. A. Voznyuk, On a Differential Game with a Random Noise [in Russian], Inst. Mat. NANU, Kiev (1992), pp. 68–74.

    Google Scholar 

  3. V. V. Ostapenko and O. M. Timoshenko, “Methods of solving differential games for different strategies of the evader,” Dokl. NAN Ukrainy, No. 6, 5–7 (1995).

    Google Scholar 

  4. L. S. Pontryagin, Selected Scientific Works [in Russian], Vol. 2, Nauka, Moscow (1988).

    Google Scholar 

  5. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  6. A. A. Chikrii, Conflict-Controlled Processes [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  7. V. G. Boltyanskii and P. S. Soltan, Combinatory Geometry of Different Classes of Convex Sets [in Russian], Shtiintsa, Kishinev (1978).

    Google Scholar 

  8. V. V. Ostapenko, “Matrix convexity,” Ukr. Mat. Zh., 47, No. 1, 64–69 (1995).

    Google Scholar 

  9. V. V. Ostapenko, “Matrix-convex functions,” Kibern. Sist. Analiz, No. 2, 112–121 (1994).

    Google Scholar 

  10. B. N. Pshenichnyi, Convex Analysis and Extremum Problems [in Russian], Nauka, Moscow (1980).

    Google Scholar 

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Authors and Affiliations

  1. T. Riskulov Kazakh Economic University, Almaty, Kazakhstan

    S. N. Amirgalieva

  2. Institute of Applied Systems Analysis, Ministry of Education and Science, National Academy of Sciences of Ukraine, National Technical University “Kiev Polytechnical Institute,”, Kiev, Ukraine

    V. V. Ostapenko

  3. Physical-Technical Institute, National Technical University “Kiev Polytechnical Institute,”, Kiev, Ukraine

    E. V. Ostapenko

Authors
  1. S. N. Amirgalieva
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  2. V. V. Ostapenko
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  3. E. V. Ostapenko
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Amirgalieva, S.N., Ostapenko, V.V. & Ostapenko, E.V. Analysis of Matrix-Convex Functions. Cybernetics and Systems Analysis 40, 547–555 (2004). https://doi.org/10.1023/B:CASA.0000047876.73283.99

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  • DOI: https://doi.org/10.1023/B:CASA.0000047876.73283.99

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