On the solution stability of parabolic optimal control problems

Alberto Domínguez Corella (), Nicolai Jork () and Vladimir M. Veliov ()
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Alberto Domínguez Corella: Vienna University of Technology
Nicolai Jork: Vienna University of Technology
Vladimir M. Veliov: Vienna University of Technology

Computational Optimization and Applications, 2023, vol. 86, issue 3, No 9, 1035-1079

Abstract: Abstract The paper investigates stability properties of solutions of optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence of the optimal solution on perturbations are obtained for problems in which the equation and the objective functional are affine with respect to the control. The perturbations may appear in both the equation and in the objective functional and may nonlinearly depend on the state and control variables. The main results are based on an extension of recently introduced assumptions on the joint growth of the first and second variation of the objective functional. The stability of the optimal solution is obtained as a consequence of a more general result obtained in the paper–the metric subregularity of the mapping associated with the system of first order necessary optimality conditions. This property also enables error estimates for approximation methods. A Lipschitz estimate for the dependence of the optimal control on the Tikhonov regularization parameter is obtained as a by-product.

Keywords: 49K20; 35K58; 49K40; 49J40 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-023-00473-4

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