Informatics and Applications
2020, Volume 14, Issue 2, pp 103
SOLUTION OF THE UNCONDITIONAL EXTREMAL PROBLEM FOR A LINEAR-FRACTIONAL INTEGRAL FUNCTIONAL DEPENDENT ON THE PARAMETER
- P. V. Shnurkov
- K. A. Adamova
Abstract
The paper is devoted to the study of the unconditional extremal problem for a fractional linear integral functional defined on a set of probability distributions. In contrast to results proved earlier, the integrands of the integral expressions in the numerator and the denominator in the problem under consideration depend on a real optimization parameter vector. Thus, the optimization problem is studied on the Cartesian product of a set of probability distributions and a set of admissible values of a real parameter vector. Three statements on the extremum of a fractional linear integral functional are proved. It is established that, in all the variants, the solution of the original problem is completely determined by the extremal properties of the test function of the linear-fractional integral functional; this function is the ratio of the integrands of the numerator and the denominator. Possible applications of the results obtained to problems of optimal control of stochastic systems are described.
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[+] About this article
Title
SOLUTION OF THE UNCONDITIONAL EXTREMAL PROBLEM FOR A LINEAR-FRACTIONAL INTEGRAL FUNCTIONAL DEPENDENT ON THE PARAMETER
Journal
Informatics and Applications
2020, Volume 14, Issue 2, pp 98-103
Cover Date
2020-06-30
DOI
10.14357/19922264200214
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
linear-fractional integral functional; unconditional extremal problem for a fractional linear integral functional; test function; optimal control problems for Markov and semi-Markov random processes
Authors
P. V. Shnurkov  and K. A. Adamova 
Author Affiliations
National Research University Higher School of Economics, 34 Tallinskaya Str., Moscow 123458, Russian Federation
Academician Pilyugin Center, 1 Vvedenskogo Str., Moscow, 117342, Russian Federation
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