Geodesic
On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 65-75
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control. 
@article{TM_2020_308_a4,
     author = {Anton O. Belyakov},
     title = {On {Sufficient} {Optimality} {Conditions} for {Infinite} {Horizon} {Optimal} {Control} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {65--75},
     year = {2020},
     volume = {308},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_308_a4/}
}
TY  - JOUR
AU  - Anton O. Belyakov
TI  - On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2020
SP  - 65
EP  - 75
VL  - 308
UR  - http://geodesic.mathdoc.fr/item/TM_2020_308_a4/
LA  - ru
ID  - TM_2020_308_a4
ER  - 
%0 Journal Article
%A Anton O. Belyakov
%T On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2020
%P 65-75
%V 308
%U http://geodesic.mathdoc.fr/item/TM_2020_308_a4/
%G ru
%F TM_2020_308_a4
Anton O. Belyakov. On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 65-75. http://geodesic.mathdoc.fr/item/TM_2020_308_a4/

[1] Acemoglu D., Introduction to modern economic growth, Princeton Univ. Press, Princeton, NJ, 2009 | Zbl

[2] S. M. Aseev, “Existence of an optimal control in infinite-horizon problems with unbounded set of control constraints”, Proc. Steklov Inst. Math., 297:Suppl. 1 (2017), 1–10 | DOI | MR

[3] Belyakov A.O., Necessary conditions for infinite horizon optimal control problems revisited, E-print, 2015, arXiv: 1512.01206 [math.OC] | Zbl

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

[5] Cartigny P., Michel P., “On a sufficient transversality condition for infinite horizon optimal control problems”, Automatica, 39:6 (2003), 1007–1010 | DOI | MR | Zbl

[6] Khlopin D., “Necessity of vanishing shadow price in infinite horizon control problems”, J. Dyn. Control Syst., 19:4 (2013), 519–552 | DOI | MR | Zbl

[7] Pickenhain S., Lykina V., “Sufficiency conditions for infinite horizon optimal control problems”, Recent advances in optimization, Proc. 12th French–German–Spanish Conf. on Optimization (Avignon, 2004), Lect. Notes Econ. Math. Syst., 563, ed. by A. Seeger, Springer, Berlin, 2006, 217–232 | DOI | MR | Zbl

[8] Seierstad A., Sydsæter K., Optimal control theory with economic applications, Adv. Textb. Econ., 24, North-Holland, Amsterdam, 1987 | MR | Zbl