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

Author

Listed:
  • 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.

Suggested Citation

  • Fabbri, Giorgio & Gozzi, Fausto & Swiech, Andrzej, 2007. "Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations," MPRA Paper 3547, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:3547
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
    4. 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.
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    Cited by:

    1. Fabbri, Giorgio & Gozzi, Fausto & Zanco, Giovanni, 2021. "Verification results for age-structured models of economic–epidemics dynamics," Journal of Mathematical Economics, Elsevier, vol. 93(C).

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    More about this item

    Keywords

    optimal control of PDE; verification theorem; dynamic programming; $epsilon$-optimal controls; Hamilton-Jacobi-Bellman equations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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