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On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions

Author

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  • J. Preininger

    (Vienna University of Technology)

  • P. T. Vuong

    (Vienna University of Technology)

Abstract

We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.

Suggested Citation

  • J. Preininger & P. T. Vuong, 2018. "On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 70(1), pages 221-238, May.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:1:d:10.1007_s10589-018-9981-6
    DOI: 10.1007/s10589-018-9981-6
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    References listed on IDEAS

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    1. Yunda Dong, 2015. "Comments on “The Proximal Point Algorithm Revisited”," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 343-349, July.
    2. Martin Seydenschwanz, 2015. "Convergence results for the discrete regularization of linear-quadratic control problems with bang–bang solutions," Computational Optimization and Applications, Springer, vol. 61(3), pages 731-760, July.
    3. Alt, Walter & Schneider, Christopher & Seydenschwanz, Martin, 2016. "Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions," Applied Mathematics and Computation, Elsevier, vol. 287, pages 104-124.
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    Cited by:

    1. Yekini Shehu & Qiao-Li Dong & Lulu Liu & Jen-Chih Yao, 2023. "Alternated inertial subgradient extragradient method for equilibrium problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 1-30, April.
    2. Yekini Shehu & Lulu Liu & Qiao-Li Dong & Jen-Chih Yao, 2022. "A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence," Networks and Spatial Economics, Springer, vol. 22(4), pages 959-990, December.
    3. Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    4. Mina Montazeri & Hamed Kebriaei & Babak N. Araabi, 2023. "A Tractable Truthful Profit Maximization Mechanism Design with Autonomous Agents," Papers 2302.05677, arXiv.org.

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