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Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations

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  • Fabbri, Giorgio
  • Gozzi, Fausto
  • Swiech, Andrzej

Abstract

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove sub- and superoptimality principles of dynamic programming and give an explicit construction of $\epsilon$-optimal controls.

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File URL: http://mpra.ub.uni-muenchen.de/3547/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3547.

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Date of creation: May 2007
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Handle: RePEc:pra:mprapa:3547

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Keywords: optimal control of PDE; verification theorem; dynamic programming; $\epsilon$-optimal controls; Hamilton-Jacobi-Bellman equations;

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  1. Gustav Feichtinger & Alexia Prskawetz & Vladimir M. Veliov, 2002. "Age-structured optimal control in population economics," MPIDR Working Papers WP-2002-045, Max Planck Institute for Demographic Research, Rostock, Germany.
  2. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
  3. Silvia Faggian & Fausto Gozzi, 2004. "On The Dynamic Programming Approach For Optimal Control Problems Of Pde'S With Age Structure," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 233-270.
  4. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
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