Stability in affine optimal control problems constrained by semilinear elliptic partial differential equations

Abstract

This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping associated with the system of first order necessary optimality conditions. Preliminary results concerning the differentiability of the functions involved are established, especially the so-called switching function. Using this ansatz, more general nonlinear perturbations are encompassed, and under weaker assumptions, than the ones previously considered in the literature on control constrained elliptic problems. Finally, the applicability of the results is illustrated with some error estimates for the Tikhonov regularization.

References in corpus (5)

• Inverse Problem for a Curved Quantum Guide
• Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz Domains
• Strong Metric Subregularity of Mappings in Variational Analysis and Optimization
• An iterative Bregman regularization method for optimal control problems with inequality constraints
• Hölder regularity in bang-bang type affine optimal control problems

Cited by in corpus (5)

• On the solution stability of parabolic optimal control problems
• New assumptions for stability analysis in elliptic optimal control problems
• Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls
• Stability and genericity of bang-bang controls in affine problems
• Solution stability of parabolic optimal control problems with fixed state-distribution of the controls