Geodesic
Minimization of a convex functional in a linear system of delay differential equations with fixed ends
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 867-877 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical method is proposed for solving the problem of moving a dynamic object described by a system of linear differential-difference equations to the origin with the minimization of a nonnegative convex functional. The method is proved to converge globally to an $\varepsilon$-optimal solution. The $\varepsilon$-optimal solution is understood as an extremal control $u(t)$, $t\in[0,T]$, that moves the system to the $\varepsilon$-neighborhood of the origin. 
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G. V. Shevchenko. Minimization of a convex functional in a linear system of delay differential equations with fixed ends. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 867-877. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a3/

[1] Bokov G. V., “Printsip maksimuma Pontryagina v zadache s vremenným zapazdyvaniem”, Fundamentalnaya i prikl. matem., 15:5 (2009), 3–19 | MR

[2] Shevchenko G. V., “Metod nakhozhdeniya optimalnogo po minimumu raskhoda resursov upravleniya dlya nelineinykh statsionarnykh sistem”, Avtomatika i telemekhanika, 70:4 (2009), 119–130 | MR | Zbl

[3] Hohenbalken B. von, “A finite algorithm to maximize certain pseudoconcave functions on polytopes”, Math. Program., 9 (1975), 189–206 | DOI | MR | Zbl