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CMFD, 2011, Volume 42, Pages 95–117 (Mi cmfd193)  

This article is cited in 1 scientific paper (total in 1 paper)

Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems

A. A. Davydovab, H. Mena-Matosc, C. S. Moreirac

a Vladimir State University, Russia
b IIASA, Austria
c Universidade do Porto and Centro de Matemática da Universidade do Porto, Portugal

Abstract: We consider the optimization problem of maximizing the time-averaged profit for the motion of a smooth polydynamical system on the circle in the presence of a smooth profit density. If the problem depends on a $k$-dimensional parameter, then the optimal averaged profit is a function of the parameter. It is known from [4] that an optimal motion can always be selected among stationary strategies and a special type of periodic motions called $level cycles$. We present a classification of all generic singularities of the optimal averaged profit if $k\le2$ and the maximum is provided by level cycles.

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English version:
Journal of Mathematical Sciences, 2014, 199:5, 510–534

Bibliographic databases:

Document Type: Article
UDC: 517.938

Citation: A. A. Davydov, H. Mena-Matos, C. S. Moreira, “Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 95–117; Journal of Mathematical Sciences, 199:5 (2014), 510–534

Citation in format AMSBIB
\Bibitem{DavMenMor11}
\by A.~A.~Davydov, H.~Mena-Matos, C.~S.~Moreira
\paper Generic profit singularities in time-averaged optimization for cyclic processes in polydynamical systems
\inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009)
\serial CMFD
\yr 2011
\vol 42
\pages 95--117
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd193}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013831}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 199
\issue 5
\pages 510--534
\crossref{https://doi.org/10.1007/s10958-014-1879-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902782655}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Davydov A.A., Mena-Matos H., Moreira C.S., “Generic Profit Singularities in Time Averaged Optimization For Phase Transitions in Polydynamical Systems”, J. Math. Anal. Appl., 424:1 (2015), 704–726  crossref  mathscinet  zmath  isi  elib  scopus
  • Современная математика. Фундаментальные направления
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