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Theorem on the Structure of the Fractionally Linear Functional Extremal Function

Author

Listed:
  • Victor Kashtanov

    (HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE), Federal State Autonomous Educational Institution for Higher Education, Higher School of Economics, National Research University, 101000 Moscow, Russia)

  • Alexander Bochkov

    (JSC NIIAS, Research and Design Institute of Information, Automation and Communication on Railway Transport, 109029 Moscow, Russia)

  • Olga Zaitseva

    (Moscow Aviation Institute, National Research University, 125993 Moscow, Russia)

Abstract

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters; hence, the problem is greatly simplified since it is reduced to the search for an extremum of some function.

Suggested Citation

  • Victor Kashtanov & Alexander Bochkov & Olga Zaitseva, 2023. "Theorem on the Structure of the Fractionally Linear Functional Extremal Function," Mathematics, MDPI, vol. 11(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2886-:d:1180745
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