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Extension technology and extrema selections in a stochastic multistart algorithm for optimal control problems

Author

Listed:
  • Alexander Yu. Gornov

    (Matrosov Institute for Systems Dynamics and Control Theory of SB RAS)

  • Tatiana S. Zarodnyuk

    (Matrosov Institute for Systems Dynamics and Control Theory of SB RAS)

  • Anton S. Anikin

    (Matrosov Institute for Systems Dynamics and Control Theory of SB RAS)

  • Evgeniya A. Finkelstein

    (Matrosov Institute for Systems Dynamics and Control Theory of SB RAS)

Abstract

The paper proposes a method for finding the minimum value of a functional in nonlinear nonconvex optimal control problems. The method takes advantage of the hidden convexity property of the controlled differential equations systems. Application of the multistart idea with extrema selection procedures makes it possible to create software that does not strongly depend on the problem size and supplies additional information about the object under investigation. Three test problems are considered to show specific properties of using the stochastic multistart algorithm and extension numerical technology.

Suggested Citation

  • Alexander Yu. Gornov & Tatiana S. Zarodnyuk & Anton S. Anikin & Evgeniya A. Finkelstein, 2020. "Extension technology and extrema selections in a stochastic multistart algorithm for optimal control problems," Journal of Global Optimization, Springer, vol. 76(3), pages 533-543, March.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:3:d:10.1007_s10898-019-00821-x
    DOI: 10.1007/s10898-019-00821-x
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    References listed on IDEAS

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    1. Alexander Yurievich Gornov & Tatiana Sergeevna Zarodnyuk, 2013. "Tunneling Algorithm for Solving Nonconvex Optimal Control Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 289-299, Springer.
    2. Alexander Yu. Gornov & Tatiana S. Zarodnyuk & Taras I. Madzhara & Anna V. Daneeva & Irina A. Veyalko, 2013. "A Collection of Test Multiextremal Optimal Control Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 257-274, Springer.
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