Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods

Markus Friedemann (), Felix Harder () and Gerd Wachsmuth ()
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Markus Friedemann: Brandenburgische Technische Universität Cottbus-Senftenberg
Felix Harder: Brandenburgische Technische Universität Cottbus-Senftenberg
Gerd Wachsmuth: Brandenburgische Technische Universität Cottbus-Senftenberg

Journal of Global Optimization, 2023, vol. 86, issue 4, No 10, 1025-1061

Abstract: 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.

Keywords: Bilevel optimal control; Inverse optimal control; Semismooth Newton; Global optimization; 49M20; 49M15; 49N45; 90C26 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-023-01288-7

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