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Vol. 49 No. 1–3 (2023)
Serdica Mathematical Journal

Articles

Solution stability of parabolic optimal control problems with fixed state-distribution of the controls

https://doi.org/10.55630/serdica.2023.49.155-186

Published 20-11-2023

  • Alberto Domínguez Corella
    • ,
  • Nicolai Jork
    • ,
  • Vladimir M. Veliov

Alberto Domínguez Corella
Vienna University of Technology

Nicolai Jork
Vienna University of Technology

Vladimir M. Veliov
Vienna University of Technology

Abstract

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The control has a predefined spacial distribution and only the magnitude at any time is a subject of choice. The obtained conditions for subregularity imply, in particular, sufficient optimality conditions that extend the known ones.

The paper is complementary to a companion one by the same authors, in which a distributed control is considered.

2020 Mathematics Subject Classification:

49N60, 49K20, 35K58

Keywords

optimal control, parabolic PDE, stability with respect to perturbations

Full text

Author Details

Alberto Domínguez Corella

Institute of Statistics and Mathematical Methods in Economics
Vienna University of Technology
1040 Vienna, Austria
alberto.corella@tuwien.ac.at

Nicolai Jork

Institute of Statistics and Mathematical Methods in Economics
Vienna University of Technology
1040 Vienna, Austria
nicolai.jork@tuwien.ac.at

Vladimir M. Veliov

Institute of Statistics and Mathematical Methods in Economics
Vienna University of Technology
1040 Vienna, Austria
vladimir.veliov@tuwien.ac.at

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