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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
as

File URL: https://mpra.ub.uni-muenchen.de/3547/1/MPRA_paper_3547.pdf
File Function: original version

## References listed on IDEAS

as
1. 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.
2. 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.
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.
Full references (including those not matched with items on IDEAS)

### Keywords

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

### JEL classification:

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

### NEP fields

This paper has been announced in the following NEP Reports:

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