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2013 | 11 | 6 | 1094-1111
Tytuł artykułu

Arrow-type sufficient conditions for optimality of age-structured control problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
6
Strony
1094-1111
Opis fizyczny
Daty
wydano
2013-06-01
online
2013-03-28
Twórcy
  • Department of Mathematics and Statistics, Tsenov Academy of Economics, Em. Chakarov str. 2, 5250, Svishtov, Bulgaria, v_krastev@mail.ru
Bibliografia
  • [1] Almeder C., Caulkins J.P., Feichtinger G., Tragler G., An age-structured single-state drug initiation model - cycles of drug epidemics and optimal prevention programs, Socio-Economic Planning Sciences, 2004, 38(1), 91–109 http://dx.doi.org/10.1016/S0038-0121(03)00030-2[Crossref]
  • [2] Aniμa S., Analysis and control of age-dependent population dynamics, Math. Model. Theory Appl., 11, Kluwer, Dordrecht, 2000
  • [3] Aniμa S., Iannelli M., Kim M.-Y., Park E.-J., Optimal harvesting for periodic age-dependent population dynamics, SIAM J. Appl. Math., 1998, 58(5), 1648–1666 http://dx.doi.org/10.1137/S0036139996301180[Crossref]
  • [4] Barucci E., Gozzi F., Technology adoption and accumulation in a vintage-capital model, Journal of Economics, 2001, 74(1), 1–38 http://dx.doi.org/10.1007/BF01231214[Crossref]
  • [5] Bazaraa M.S., Shetty C.M., Nonlinear Programming, Mir, Moscow, 1982 (in Russian)
  • [6] Behrens D.A., Caulkins J.P., Tragler G., Feichtinger G., Optimal control of drug epidemics: prevent and treat - but not at the same time?, Management Science, 2000, 46(3), 333–347 http://dx.doi.org/10.1287/mnsc.46.3.333.12068[Crossref]
  • [7] Brokate M., Pontryagin’s principle for control problems in age-dependent population dynamics, J. Math. Biol., 1985, 23(1), 75–101 http://dx.doi.org/10.1007/BF00276559[Crossref]
  • [8] Carlson D.A., Uniformly overtaking and weakly overtaking optimal solutions in infinite-horizon optimal control: when optimal solutions are agreeable, J. Optim. Theory Appl., 1990, 64(1), 55–69 http://dx.doi.org/10.1007/BF00940022[Crossref]
  • [9] Carlson D.A., Haurie A.B., Leizarowitz A., Infinite Horizon Optimal Control, 2nd ed., Springer, Berlin-Heidelberg-New York, 1991 http://dx.doi.org/10.1007/978-3-642-76755-5
  • [10] Crampin M., Pirani F.A.E., Applicable Differential Geometry, London Math. Soc. Lecture Note Ser., 59, Cambridge University Press, Cambridge, 1986
  • [11] Faggian S., Grosset L., Optimal investment in age-structured goodwill, preprint available at http://dx.doi.org/10.2139/ssrn.2097829 [Crossref]
  • [12] Feichtinger G., Hartl R.F., Kort P.M., Veliov V.M., Anticipation effects of technological progress on capital accumulation: a vintage capital approach, J. Econom. Theory, 2006, 126(1), 143–164 http://dx.doi.org/10.1016/j.jet.2004.10.001[Crossref]
  • [13] Feichtinger G., Hartl R.F., Kort P.M., Veliov V.M., Capital accumulation under technological progress and learning: A vintage capital approach, European J. Oper. Res., 2006, 172(1), 293–310 http://dx.doi.org/10.1016/j.ejor.2004.07.070[Crossref]
  • [14] Feichtinger G., Tragler G., Veliov V.M., Optimality conditions for age-structured control systems, J. Math. Anal. Appl., 2003, 288(1), 47–68 http://dx.doi.org/10.1016/j.jmaa.2003.07.001[Crossref]
  • [15] Fichtenholz G.M., A course of differential and integral calculus, I, 8th ed., Fizmatlit, Moscow, 2003 (in Russian)
  • [16] Grosset L., Viscolani B., Advertising for the introduction of an age-sensitive product, Optimal Control Appl. Methods, 2005, 26(3), 157–167 http://dx.doi.org/10.1002/oca.758[Crossref]
  • [17] Hardy G.H., Littlewood J.E., Pólya G., Inequalities, Cambridge Math. Lib., Cambridge University Press, Cambridge, 1934
  • [18] Hartl R.F., Kort P.M., Feichtinger G., Offence control taking into account heterogeneity of age, J. Optim. Theory Appl., 2003, 116(3), 591–620 http://dx.doi.org/10.1023/A:1023017403842[Crossref]
  • [19] Haurie A., Sethi S., Hartl R., Optimal control of an age-structured population model with applications to social services planning, Large Scale Systems, 1984, 6(2), 133–158
  • [20] Ioffe A.D., Tikhomirov V.M., Theory of Extremal Problems, Series in Nonlinear Analysis and its Applications, Nauka, Moscow, 1974 (in Russian)
  • [21] Pontryagin L.S., Ordinary Differential Equations, 4th ed., Nauka, Moscow, 1974 (in Russian)
  • [22] Prskawetz A., Tsachev T., Veliov V.M., Optimal education in an age-structured model under changing labor demand and supply, Macroecon. Dyn., 16(2), 159–183 [WoS]
  • [23] Seierstad A., Sydsæter K., Sufficient conditions in optimal control theory, Internat. Econom. Rev., 1977, 18(2), 367–391 http://dx.doi.org/10.2307/2525753[Crossref]
  • [24] Seierstad A., Sydsæter K., Optimal Control Theory with Economic Applications, Adv. Textbooks Econom., 24, Elsevier, Amsterdam, 2002
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0219-7
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