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Necessary optimality conditions for improper infinite-horizon control problems. (English) Zbl 1306.49033

Klatte, Diethard (ed.) et al., Operations research proceedings 2011. Selected papers of the international conference on operations research (OR 2011), August 30 – September 2, 2011, Zurich, Switzerland. Berlin: Springer (ISBN 978-3-642-29209-5/pbk; 978-3-642-29210-1/ebook). Operations Research Proceedings, 21-26 (2012).
Summary: The paper revisits the issue of necessary optimality conditions for infinitehorizon optimal control problems. It is proved that the normal form maximum principle holds with an explicitly specified adjoint variable if an appropriate relation between the discount rate, the growth rate of the solution and the growth rate of the objective function is satisfied. The main novelty is that the result applies to general non-stationary systems and the optimal objective value needs not be finite (in which case the concept of overtaking optimality is employed).
For the entire collection see [Zbl 1250.90010].

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49J99 Existence theories in calculus of variations and optimal control
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