Sufficiency Conditions for Infinite Horizon Optimal Control Problems

Sabine Pickenhain () and Valeriya Lykina ()
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Sabine Pickenhain: Brandenburg University of Technology Cottbus
Valeriya Lykina: Brandenburg University of Technology Cottbus

A chapter in Recent Advances in Optimization, 2006, pp 217-232 from Springer

Abstract: Summary In this paper we formulate and use the duality concept of Klötzler (1977) for infinite horizon optimal control problems. The main idea is choosing weighted Sobolev and weighted Lp spaces as the state and control spaces, respectively. Different criteria of optimality are known for specific problems, e.g. the overtaking criterion of von Weizsäcker (1965), the catching up criterion of Gale (1967) and the sporadically catching up criterion of Halkin (1974). Corresponding to these criteria we develop the duality theory and prove sufficient conditions for local optimality. Here we use some remarkable properties of weighted spaces. An example is presented where the solution is obtained in the framework of these weighted spaces, but which does not belong to standard Sobolev spaces.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-28258-7_14

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DOI: 10.1007/3-540-28258-0_14

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