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A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

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  • Eduardo Casas
  • Fredi Tröltzsch

Abstract

A theorem on error estimates for smooth nonlinear programming problems in Banach spaces is proved that can be used to derive optimal error estimates for optimal control problems. This theorem is applied to a class of optimal control problems for quasilinear elliptic equations. The state equation is approximated by a finite element scheme, while different discretization methods are used for the control functions. The distance of locally optimal controls to their discrete approximations is estimated. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Eduardo Casas & Fredi Tröltzsch, 2012. "A general theorem on error estimates with application to a quasilinear elliptic optimal control problem," Computational Optimization and Applications, Springer, vol. 53(1), pages 173-206, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:173-206
    DOI: 10.1007/s10589-011-9453-8
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    Cited by:

    1. Moritz Keuthen & Michael Ulbrich, 2015. "Moreau–Yosida regularization in shape optimization with geometric constraints," Computational Optimization and Applications, Springer, vol. 62(1), pages 181-216, September.
    2. Malte Braack & Martin F. Quaas & Benjamin Tews & Boris Vexler, 2018. "Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 950-972, September.
    3. Bui Trong Kien & Arnd Rösch & Nguyen Hai Son & Nguyen Van Tuyen, 2023. "FEM for Semilinear Elliptic Optimal Control with Nonlinear and Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 130-173, April.
    4. Eduardo Casas & Mariano Mateos & Arnd Rösch, 2018. "Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity," Computational Optimization and Applications, Springer, vol. 70(1), pages 239-266, May.

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