A factorization with update procedures for a KKT matrix arising in direct optimal control

  • Quadratic programs obtained for optimal control problems of dynamic or discrete-time processes usually involve highly block structured Hessian and constraints matrices, to be exploited by efficient numerical methods. In interior point methods, this is elegantly achieved by the widespread availability of advanced sparse symmetric indefinite factorization codes. For active set methods, however, conventional dense matrix techniques suffer from the need to update base matrices in every active set iteration, thereby loosing the sparsity structure after a few updates. This contribution presents a new factorization of a KKT matrix arising in active set methods for optimal control. It fully respects the block structure without any fill-in. For this factorization, matrix updates are derived for all cases of active set changes. This allows for the design of a highly efficient block structured active set method for optimal control and model predictive control problems with long horizons or many control parameters.

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Metadaten
Author:Christian Kirches, Hans Georg Bock, Johannes P. Schlöder, Sebastian Sager
DOI:https://doi.org/10.1007/s12532-011-0030-z
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2011
Tag:Software; Theoretical Computer Science
Volume:3
Issue:4
Page Number:30
First Page:319
Last Page:348
Mathematical Programming Computation :MPC 2011 - Issue 4
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