Osmolovskii, N. P., & Veliov, V. (2023). On the Strong Subregularity of the Optimality Mapping in an Optimal Control Problem with Pointwise Inequality Control Constraints. Applied Mathematics and Optimization, 87(3), Article 43. https://doi.org/10.1007/s00245-022-09959-9
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Applied Mathematics and Optimization
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ISSN:
0095-4616
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Date (published):
13-Mar-2023
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Number of Pages:
29
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Publisher:
Springer Nature
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Peer reviewed:
Yes
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Keywords:
Control constraint; Mayer’s problem; Optimal control; Optimization; metric subregularity
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Abstract:
This paper presents sufficient conditions for strong metric subregularity (SMsR) of the optimality mapping associated with the local Pontryagin maximum principle for Mayer-type optimal control problems with pointwise control constraints given by a finite number of inequalities Gj(u)≤0 . It is assumed that all data are twice smooth, and that at each feasible point the gradients Gj'(u) of the active constraints are linearly independent. The main result is that the second-order sufficient optimality condition for a weak local minimum is also sufficient for a version of the SMSR property, which involves two norms in the control space in order to deal with the so-called two-norm-discrepancy.
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Project title:
Optimale Steuerung mit endlichen Steuerungsmengen und Anwendungen in der Modelbasierten Regelung: P 31400-N32 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
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