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Optimal control of counter-terrorism tactics

Author

Listed:
  • Bayón, L.
  • Fortuny Ayuso, P.
  • García-Nieto, P.J.
  • Grau, J.M.
  • Ruiz, M.M.

Abstract

This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality.

Suggested Citation

  • Bayón, L. & Fortuny Ayuso, P. & García-Nieto, P.J. & Grau, J.M. & Ruiz, M.M., 2019. "Optimal control of counter-terrorism tactics," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 477-491.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:477-491
    DOI: 10.1016/j.amc.2018.11.022
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    2. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
    3. Moshe Kress & Roberto Szechtman, 2009. "Why Defeating Insurgencies Is Hard: The Effect of Intelligence in Counterinsurgency Operations---A Best-Case Scenario," Operations Research, INFORMS, vol. 57(3), pages 578-585, June.
    4. Keohane, Nathaniel O & Zeckhauser, Richard J, 2003. "The Ecology of Terror Defense," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 201-229, March-May.
    5. Tsur, Yacov & Zemel, Amos, 2001. "The infinite horizon dynamic optimization problem revisited: A simple method to determine equilibrium states," European Journal of Operational Research, Elsevier, vol. 131(3), pages 482-490, June.
    6. Firdaus Udwadia & George Leitmann & Luca Lambertini, 2006. "A dynamical model of terrorism," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-32, September.
    7. Friedrich Schneider & Tilman Brück & Daniel Meierrieks, 2015. "The Economics Of Counterterrorism: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 131-157, February.
    8. Seidl, Andrea & Kaplan, Edward H. & Caulkins, Jonathan P. & Wrzaczek, Stefan & Feichtinger, Gustav, 2016. "Optimal control of a terror queue," European Journal of Operational Research, Elsevier, vol. 248(1), pages 246-256.
    9. João Ricardo Faria & Daniel Arce, 2012. "Counterterrorism And Its Impact On Terror Support And Recruitment: Accounting For Backlash," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 431-445, October.
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