Journal of Optimization Theory and Applications

, Volume 167, Issue 1, pp 243–271 | Cite as

On the Infinite-Horizon Optimal Control of Age-Structured Systems

  • B. Skritek
  • V. M. VeliovEmail author


The paper presents necessary optimality conditions of Pontryagin’s type for infinite-horizon optimal control problems for age-structured systems with state- and control-dependent boundary conditions. Despite the numerous applications of such problems in population dynamics and economics, a “complete” set of optimality conditions is missing in the existing literature, because it is problematic to define in a sound way appropriate transversality conditions for the corresponding adjoint system. The main novelty is that (building on recent results by Aseev and the second author) the adjoint function in the Pontryagin principle is explicitly defined, which avoids the necessity of transversality conditions. The result is applied to several models considered in the literature.


Age-structured systems Infinite-horizon optimal control  Pontryagin’s maximum principle Population dynamics  Vintage economic models 

Mathematics Subject Classification

49K20 93C20 91B99 35F15 



This research was supported by the Austrian Science Foundation (FWF) under Grant No. I 476-N13.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.ORCOS, Institute of Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

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