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Optimality Conditions for Optimal Control of the Monodomain Model with Pointwise Control and State Constraints

Author

Listed:
  • Maria Robert

    (National Institute of Technology Calicut)

  • Suresh Kumar Nadupuri

    (National Institute of Technology Calicut)

  • Nagaiah Chamakuri

    (IISER Thiruvananthapuram
    IISER Thiruvananthapuram)

Abstract

This work deals with the theoretical study of the optimality conditions for the optimal control of the monodomain model arising in cardiac electrophysiology with mixed control-state constraints. The monodomain model is a coupled system of reaction–diffusion equation with cubic nonlinearity in the reaction term and an ordinary differential equation. The existence of optimal control is established, and the twice Fréchet differentiability of the control-to-state operator is discussed. The first-order necessary optimality condition is derived. Most significantly, a detailed proof of the sufficient second-order optimality condition is demonstrated with mixed control-state constraints.

Suggested Citation

  • Maria Robert & Suresh Kumar Nadupuri & Nagaiah Chamakuri, 2024. "Optimality Conditions for Optimal Control of the Monodomain Model with Pointwise Control and State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 605-627, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02440-3
    DOI: 10.1007/s10957-024-02440-3
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    References listed on IDEAS

    as
    1. Chamakuri, Nagaiah & Kunisch, Karl, 2017. "Primal-dual active set strategy for large scale optimization of cardiac defibrillation," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 178-193.
    2. Chamakuri Nagaiah & Karl Kunisch & Gernot Plank, 2011. "Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology," Computational Optimization and Applications, Springer, vol. 49(1), pages 149-178, May.
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