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Recent Advances in Optimization pp 217–232Cite as

Sufficiency Conditions for Infinite Horizon Optimal Control Problems

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 563))

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.

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Author information

Authors and Affiliations

  1. Brandenburg University of Technology Cottbus, Germany

    Sabine Pickenhain & Valeriya Lykina

Authors
  1. Sabine Pickenhain
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  2. Valeriya Lykina
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Avignon, 33, rue Louis Pasteur, 84000, Avignon, France

    Alberto Seeger

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© 2006 Springer-Verlag Berlin Heidelberg

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Pickenhain, S., Lykina, V. (2006). Sufficiency Conditions for Infinite Horizon Optimal Control Problems. In: Seeger, A. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28258-0_14

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