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September 29, 2025Open Access

State-based nested iteration solution of optimal control problems with PDE constraints

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Authors

ULUlrich LangerRLRichard LöscherOSOlaf Steinbach

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Overview

This analysis demonstrates an effective approach to optimize control in systems governed by PDEs, suggesting improved accuracy and cost-efficiency.

Key Points

  • The study offers a novel solution for optimal control problems with partial differential equations, improving computational efficiency.
  • An optimal relationship between regularization parameters and mesh size was established, enhancing accuracy in control systems.
  • The methods discussed include discretization of parabolic and hyperbolic PDEs through finite element approaches, ensuring robustness.
  • Results indicate that the proposed state-based nested iteration method achieves asymptotically optimal complexity in computations.

Cite This Study

Langer et al. (2025) studied this question.

synapsesocial.com/papers/68da58dcc1728099cfd112cchttps://doi.org/10.48550/arxiv.2505.19062
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