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arXiv · 2409.19347

Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations

Cung The Anh·Nguyen Hai Ha Giang
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Abstract

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form were proved for a distributed optimal control problem governed by the three-dimensional viscous Camassa-Holm equations in bounded domains with the cost functional of a quite general form and pointwise control constraints. We will establish the second-order sufficient optimality conditions as well as the Lipschitz stability results of the control system with respect to perturbations of the initial data.

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Cung The Anh, Nguyen Hai Ha Giang. 2024-09-28. Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations. https://arxiv.org/abs/2409.19347

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