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 Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 4, Pages 752–769 (Mi izv925)

Sufficient optimality conditions for linear differential inequalities with discontinuous trajectories

V. Z. Belen'kii

Central Economics and Mathematics Institute, RAS

Abstract: This article contains a formalization of the linear differential problem of optimal control with discontinuous trajectories in the form of a linear programming (LP) problem in a partially ordered space. This enables us to construct a dual LP problem and to obtain on this basis a sufficient criterion for optimality. The main idea in the construction of a dual pair of LP-problems consists in the introduction of an orientation in the space of piecewise continuous functions (left for the direct problem and right for the dual problem). The author thinks that the proposed criterion is close to necessary (for the class of functions under consideration), although he has not been able to prove it. The method of using the criterion for actually finding optimal trajectories is illustrated with an example; this method has actually been used by the author earlier to solve problems of an applied nature.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:1, 39–54

Bibliographic databases:

UDC: 517.97
MSC: Primary 49K24, 49M35; Secondary 34A40, 49K15

Citation: V. Z. Belen'kii, “Sufficient optimality conditions for linear differential inequalities with discontinuous trajectories”, Izv. RAN. Ser. Mat., 56:4 (1992), 752–769; Russian Acad. Sci. Izv. Math., 41:1 (1993), 39–54

Citation in format AMSBIB
\Bibitem{Bel92} \by V.~Z.~Belen'kii \paper Sufficient optimality conditions for linear differential inequalities with discontinuous trajectories \jour Izv. RAN. Ser. Mat. \yr 1992 \vol 56 \issue 4 \pages 752--769 \mathnet{http://mi.mathnet.ru/izv925} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1208149} \zmath{https://zbmath.org/?q=an:0801.49021} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41...39B} \transl \jour Russian Acad. Sci. Izv. Math. \yr 1993 \vol 41 \issue 1 \pages 39--54 \crossref{https://doi.org/10.1070/IM1993v041n01ABEH002250} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LZ84700002}