title: Adjoint-based algorithms and numerical methods for sensitivity generation and optimization of large scale dynamic systems
creator: Albersmeyer, Jan
subject: ddc-510
subject: 510 Mathematics
description: This thesis presents advances in numerical methods for the solution of optimal control problems. In particular, the new ideas and methods  presented in this thesis contribute to the research fields of structure-exploiting Newton-type methods for large scale nonlinear programming and sensitivity generation for IVPs for ordinary differential equations and differential algebraic equations. Based on these contributions, a new lifted adjoint-based partially reduced exact-Hessian SQP (L-PRSQP) method for nonlinear multistage constrained  optimization problems with large scale differential algebraic process models is proposed. It is particularly well suited for optimization problems which involve many state variables in the dynamic process but only few degrees of freedom, i.e., controls, parameter or free initial values. This L-PRSQP method can be understood as an extension of the work of Schäfer to the case of exact-Hessian SQP methods, making use of directional forward/adjoint sensitivities of second order. It stands hence in the tradition of the direct multiple shooting approaches for differential algebraic equations of index 1 of Bock and co-workers. To the novelties that are presented in this thesis further belong - the generalization of the direct multiple shooting idea to structure-exploiting algorithms for NLPs with an internal chain structure of the problem functions, - an algorithmic trick that allows these so-called lifted methods to compute the condensed subproblems directly based on minor modifications to the user given problem functions and without further knowledge on the internal structure of the problem, - a lifted adjoint-based exact-Hessian SQP method that is shown to be equivalent to a full-space approach, but only has the complexity of an unlifted/single shooting approach per iteration, - new adjoint schemes for sensitivity generation based on Internal Numerical Differentiation (IND) for implicit LMMs using the example of Backward Differentiation Formulas (BDF), - the combination of univariate Taylor coefficient (TC) propagation and IND, resulting in IND-TC schemes which allow for the first time the efficient computation of directional forward and forward/adjoint sensitivities of arbitrary order, - a strategy to propagate directional sensitivities of arbitrary order across switching events in the integration, - a local error control strategy for sensitivities and a heuristic global error estimation strategy for IVP solutions in connection with IND schemes, - the software packages DAESOL-II and SolvIND, implementing the ideas related to IVP solution and sensitivity generation, as well as the software packages LiftOpt and DynamicLiftOpt that implement the lifted Newton-type methods for general NLP problems and the L-PRSQP method in the optimal control context, respectively. The performance of the presented approaches is demonstrated by the practical application of our codes to a series of numerical test problems and by comparison to the performance of alternative state-of-the-art approaches, if applicable. In particular, the new lifted adjoint-based partially reduced exact-Hessian SQP method allows the efficient and successful solution of a practical optimal control problem for a binary distillation column, for which the solution using a direct multiple shooting SQP method with an exact-Hessian would have been prohibitively expensive until now.
date: 2010
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/11651/1/dissertation_published.pdf
identifier: DOI:10.11588/heidok.00011651
identifier: urn:nbn:de:bsz:16-opus-116512
identifier:   Albersmeyer, Jan  (2010) Adjoint-based algorithms and numerical methods for sensitivity generation and optimization of large scale dynamic systems.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/11651/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng