Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/308989 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 86 [Issue:] 4 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 1025-1061
Publisher: 
Springer US, New York, NY
Abstract: 
We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem. The reformulated problem is nonconvex and standard regularity conditions like Robinson's CQ are violated. Via a relaxation of the constraints, the problem can be decomposed into a family of convex problems and this is the basis for a solution algorithm. The convergence properties are analyzed. It is shown that a penalty method can be employed to solve this family of problems while maintaining convergence speed. For an example problem, the use of the identity as penalty function allows for the solution by a semismooth Newton method. Numerical results are presented. Difficulties and limitations of our approach to solve a nonconvex problem to global optimality are discussed.
Subjects: 
Bilevel optimal control
Inverse optimal control
Semismooth Newton
Global optimization
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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