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International Conference on Large-Scale Scientific Computing

LSSC 2013: Large-Scale Scientific Computing pp 143–151Cite as

Pontryagin’s Type Optimality Conditions for a Distributed Control Problem Arising in Endogenous Growth Theory

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8353))

Abstract

The paper presents an optimality condition for a distributed optimal control problem arising in economics, where the (one-dimensional) spatial domain can be influenced by the control. The result enables analytical and numerical investigation of a class of endogenous growth models with investment-dependent technological frontier and heterogeneous capital stock.

This research was funded by the Austrian Science Foundation (FWF) under grant No I 476-N13.

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Notes

  1. 1.

    The rest of the existing literature on optimal control of heterogeneous systems (see e.g. [6] and the bibliography therein) does not cover problems with endogenously changing spatial domain.

References

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  3. Belyakov, A., Tsachev, Ts., Veliov, V.M.: Optimal control of heterogeneous systems with endogenous domain of heterogeneity. Appl. Math. Optim. 64(2), 287–311 (2011)

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  4. Sorger, G.: Horizontal innovations with endogenous quality choice. Economica 78, 697–722 (2011)

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  5. Strauss, A.: Continuous dependence of solutions of ordinary differential equations. Am. Math. Mon. 71(6), 649–652 (1964)

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  6. Veliov, V.M.: Optimal control of heterogeneous systems: basic theory. J. Math. Anal. Appl. 346, 227–242 (2008)

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Author information

Authors and Affiliations

  1. Institute of Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria

    Bernhard Skritek & Vladimir M. Veliov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Tsvetomir Tsachev

Authors
  1. Bernhard Skritek
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  2. Tsvetomir Tsachev
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  3. Vladimir M. Veliov
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Corresponding author

Correspondence to Tsvetomir Tsachev .

Editor information

Editors and Affiliations

  1. Inst. of Info. & Comm. Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

  3. Dept. of Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Skritek, B., Tsachev, T., Veliov, V.M. (2014). Pontryagin’s Type Optimality Conditions for a Distributed Control Problem Arising in Endogenous Growth Theory. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_15

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  • DOI: https://doi.org/10.1007/978-3-662-43880-0_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43879-4

  • Online ISBN: 978-3-662-43880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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