Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A primal-dual active set algorithm for bilaterally control constrained optimal control problems


Author: Michael Hintermüller
Journal: Quart. Appl. Math. 61 (2003), 131-160
MSC: Primary 49M37; Secondary 49J20, 49M29
DOI: https://doi.org/10.1090/qam/1955227
MathSciNet review: MR1955227
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Abstract: A generalized Moreau-Yosida based primal-dual active set algorithm for the solution of a representative class of bilaterally control constrained optimal control problems with boundary control is developed. The use of the generalized Moreau-Yosida approximation allows an efficient identification of the active and inactive sets at each iteration level. The method requires no step-size strategy and exhibits a finite termination property for the discretized problem class. In infinite as well as in finite dimensions a convergence analysis based on an augmented Lagrangian merit function is given. In a series of numerical tests the efficiency of the new algorithm is emphasized.


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DOI: https://doi.org/10.1090/qam/1955227
Article copyright: © Copyright 2003 American Mathematical Society


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