Arrow-type sufficient conditions for optimality of age-structured control problems
Vladimir Krastev
Open Mathematics, Tome 11 (2013), p. 1094-1111 / Harvested from The Polish Digital Mathematics Library

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).

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269778
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     author = {Vladimir Krastev},
     title = {Arrow-type sufficient conditions for optimality of age-structured control problems},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {1094-1111},
     zbl = {1275.49038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0219-7}
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Vladimir Krastev. Arrow-type sufficient conditions for optimality of age-structured control problems. Open Mathematics, Tome 11 (2013) pp. 1094-1111. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0219-7/

[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] | Zbl 0935.92030

[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] | Zbl 1026.91073

[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] | Zbl 1231.93065

[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] | Zbl 0599.92017

[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] | Zbl 0687.49023

[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 | Zbl 0758.49001

[10] Crampin M., Pirani F.A.E., Applicable Differential Geometry, London Math. Soc. Lecture Note Ser., 59, Cambridge University Press, Cambridge, 1986 | Zbl 0606.53001

[11] Faggian S., Grosset L., Optimal investment in age-structured goodwill, preprint available at http://dx.doi.org/10.2139/ssrn.2097829 [Crossref] | Zbl 1276.90035

[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] | Zbl 1108.91055

[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] | Zbl 1116.91033

[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] | Zbl 1042.49035

[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] | Zbl 1029.49034

[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 | Zbl 0565.90035

[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] | Zbl 1246.91092

[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] | Zbl 0392.49010

[24] Seierstad A., Sydsæter K., Optimal Control Theory with Economic Applications, Adv. Textbooks Econom., 24, Elsevier, Amsterdam, 2002 | Zbl 0613.49001