Cent. Eur. J. Math. • 11(6) • 2013 • 1094-1111 DOI: 10.2478/s11533-013-0219-7 Arrow-type sufficient conditions for optimality of age-structured control problems Vladimir Y. Krastev 1∗ 1 Department of Mathematics and Statistics, Tsenov Academy of Economics, Em. Chakarov str. 2, 5250, Svishtov, Bulgaria 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). 49K20, 49K21 Age-structured optimal control • Sufficient conditions for optimality © Versita Sp. z o.o. 1. Introduction and the general model Age-structured optimal control theory serves to study problems arising in different areas such as epidemiology [1], harvesting [2, 3], investment in capital goods [4, 12, 13], investment in human capital [22], and marketing [11, 16]. Solutions of these problems are often obtained by applying necessary optimality conditions of Pontryagin type. For the most general age-structured model, in which the individuals have finite lifetimes, these types of optimality conditions are obtained in [14]. An earlier contribution, which is addressed to a particular case of the general age-structured model, can be found in [7] (see [7, 14] for references to applications). Two basic approaches are used to supplement a necessary optimality condition when solving an optimization problem. One of them consists of proving the existence of a solution, in the case of age-structured optimal control such a result can be found for example in [2, p. 68]. The other approach is to find sufficient conditions that guarantee that the solution is indeed optimal. For optimal control problems for ODEs, such conditions can be found in [23, 24]. As in optimal control ∗ E-mail: v_krastev@mail.ru Unauthenticated Download Date | 7/28/18 5:27 AM