Korean J. Math.  Vol 23, No 2 (2015)  pp.283-291
DOI: https://doi.org/10.11568/kjm.2015.23.2.283

Value function and optimality conditions

Kyung Eung Kim


In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.


Value function, Optimal conditions, Generalized derivatives.

Subject classification

49J21, 49K21.


Full Text:



J. P. Aubin and A. Cellina, Differential Inclusion, Springer-Verlag, Gru ̈ndlehren der Math. Wiss. (1984). (Google Scholar)

J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkh ̈auser, Boston, Basel, Berlin, (1990). (Google Scholar)

P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in optimal control theory, SIAM J. Control Optim. 29 (1991), 1322–1347. (Google Scholar)

F. H. Clarke, A general theorem on necessary conditions in optimal control, J. Discret. Contin. Dyn. Syst. 29 (2011), 485–503. (Google Scholar)

H. Frankowska, Optimal Trajectories Associated to a Solution of Contingent Hamilton-Jacobi Equation, Applied Mathematics and Optimization 19 (1993), 291– 311. (Google Scholar)

R. Vinter Optimal Control, Birkh ̈auser, Boston, (2000). (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr