On the problem of optimal stimulation of demand
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 2, pp. 23-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of optimal stimulation of demand based on a controlled version of Kaldor's business cycle model. Using the approximation method, we prove a version of Pontryagin's maximum principle in the normal form, containing an additional pointwise condition on the adjoint variable. The results obtained develop and strengthen the previous results in this direction.
Keywords: optimal control, Kaldor's business cycle model, Pontryagin's maximum principle.
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A. S. Aseev; S. P. Samsonov. On the problem of optimal stimulation of demand. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 2, pp. 23-38. http://geodesic.mathdoc.fr/item/TIMM_2024_30_2_a1/

[1] Ramsey F.P., “A mathematical theory of saving”, The Economic Journal, 38 (1928), 543–559 | DOI

[2] Barro R.Dzh., Sala-i-Martin Kh., Ekonomicheskii rost, BINOM. Laboratoriya znanii, M., 2010, 824 pp.

[3] Acemoglu D., Introduction to modern economic growth, Princeton Univ. Press, Princeton, NJ, 2008, 1008 pp.

[4] Carlson D.A., Haurie A.B., Leizarowitz A., Infinite horizon optimal control, Deterministic and stochastic systems, Springer-Verlag, Berlin, 1991, 332 pp. | DOI | MR | Zbl

[5] Aseev A.S., “Optimal economic growth problem”, J. Math. Sci., 276 (2023), 37–47 | DOI | MR | Zbl

[6] Kaldor N., “A model of trade cycle”, The Economic Journal, 50:197 (1940), 78–92 | DOI

[7] Aseev A.S., “Optimalnye statsionarnyi rezhimy v upravlyaemoi modeli biznes-tsikla Kaldora”, Mat. modelirovanie, 31:2 (2019), 33–47 | DOI | Zbl

[8] Aseev S.M., Kryazhimskii A.V., “Printsip maksimuma Pontryagina i zadachi optimalnogo ekonomicheskogo rosta”, Tr. MIAN, 257 (2007), 3–271

[9] Weitzman M.J., Income, wealth, and the maximum principle, Harvard University Press, Cambridge, MA, 2003, 358 pp.

[10] Seierstad A., Sydsæter K., Optimal control theory with economic applications, North-Holland, Amsterdam, 1987, 472 pp. | MR | Zbl

[11] Aseev S.M., Besov K.O., Kryazhimskii A.V., “Zadachi optimalnogo upravleniya na beskonechnom intervale vremeni v ekonomike”, Uspekhi mat. nauk, 67:2 (2012), 3–64 | DOI | MR | Zbl

[12] Aseev S.M., Veliov V.M., “Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:3 (2014), 41–57 | MR

[13] Pickenhain S., “Infinite horizon optimal control problems in the light of convex analysis in Hilbert spaces”, J. Set-Valued Var. Anal., 23:1 (2015), 169–189 | DOI | MR | Zbl

[14] Tauchnitz N., “The Pontryagin maximum principle for nonlinear optimal control problems with infinite horizon”, J. Optim. Theory Appl., 167:1 (2015), 27–48 | DOI | MR | Zbl

[15] Cannarsa P., Frankowska H., “Value function, relaxation, and transversality conditions in infinite horizon optimal control”, J. Math. Anal. Appl., 457 (2018), 1118–1217 | DOI | MR

[16] Ye J.J., “Nonsmooth maximum principle for infinite-horizon problems”, J. Optim. Theory Appl., 76:3 (1993), 485–500 | DOI | MR | Zbl

[17] Cesari L., Optimization — theory and applications, Problems with ordinary differential equations, Springer-Verlag, NY, 1983 | DOI | MR | Zbl

[18] Kolmogorov A.N., Fomin S.V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, Glavnaya redaktsiya fiz.-mat. lit., M., 1976, 544 pp. | MR

[19] Clarke F.H., Optimization and nonsmooth analysis, J. Wiley, NY, 1983, 308 pp. | MR | Zbl

[20] Filippov A.F., “O nekotorykh voprosakh teorii optimalnogo regulirovaniya”, Vestn. Moskov. universiteta, 1959, no. 2, 25–32 | Zbl

[21] Khartman F., Obyknovennye differentsialnyi uravneniya, Mir, M., 1970, 720 pp.