Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/313354 
Year of Publication: 
2023
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 85 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 479-508
Publisher: 
Springer US, New York, NY
Abstract: 
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-order necessary optimality conditions are established. The aforementioned results require the controls to be functions in H1and subject to pointwise lower and upper bounds. In order to obtain the Newton differentiability of the optimality conditions, we employ a Moreau–Yosida-type penalty approach to treat the control constraint and study its convergence. The first-order optimality conditions of the regularized problems are shown to be Newton differentiable, and a generalized Newton method is detailed. A discretization of the optimal control problem by piecewise linear finite elements is proposed and numerical results are presented.
Subjects: 
PDE-constrained optimization
Optimal control
Nonlocal equation
Kirchhoff equation
Quasilinear equation
Semismooth Newton method
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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