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• W2562149025 abstract "In this thesis we develop algorithms for the numerical solution of problems from nonlinearoptimum experimental design (OED) for parameter estimation in differential–algebraicequations. These OED problems can be formulated as special types of path- and control-constrained optimal control (OC) problems. The objective is to minimize a functional onthe covariance matrix of the model parameters that is given by first-order sensitivities of themodel equations. Additionally, the objective is nonlinearly coupled in time, which makeOED problems a challenging class of OC problems. For their numerical solution, we proposea direct multiple shooting parameterization to obtain a structured nonlinear programmingproblem (NLP). An augmented system of nominal and variational states for the modelsensitivities is parameterized on multiple shooting intervals and the objective is decoupledby means of additional variables and constraints. In the resulting NLP, we identify severalstructures that allow to evaluate derivatives at greatly reduced costs compared to a standardOC formulation.For the solution of the block-structured NLPs, we develop a new sequential quadraticprogramming (SQP) method. Therein, partitioned quasi-Newton updates are used to approximate the block-diagonal Hessian of the Lagrangian. We analyze a model problem withindefinite, block-diagonal Hessian and prove that positive definite approximations of theindividual blocks prevent superlinear convergence. For an OED model problem, we showthat more and more negative eigenvalues appear in the Hessian as the multiple shooting gridis refined and confirm the detrimental impact of positive definite Hessian approximations.Hence, we propose indefinite SR1 updates to guarantee fast local convergence. We developa filter line search globalization strategy that accepts indefinite Hessians based on a newcriterion derived from the proof of global convergence. BFGS updates with a scaling strategy to prevent large eigenvalues are used as fallback if the SR1 update does not promoteconvergence. For the solution of the arising sparse and nonconvex quadratic subproblems, aparametric active set method with inertia control within a Schur complement approach isdeveloped. It employs a symmetric, indefinite LBL T -factorization for the large, sparse KKTmatrix and maintains and updates QR-factors of a small and dense Schur complement.The new methods are complemented by two C++ implementations: muse transforms anOED or OC problem instance to a structured NLP by means of direct multiple shooting.A special feature is that fully independent grids for controls, states, path constraints, andmeasurements are maintained. This provides higher flexibility to adapt the NLP formulationto the characteristics of the problem at hand and facilitates comparison of different formulations in the light of the lifted Newton method. The software package blockSQP is animplementation of the new SQP method that uses a newly developed variant of the quadraticprogramming solver qpOASES. Numerical results are presented for a benchmark collection ofOED and OC problems that show how SR1 approximations improve local convergence overBFGS. The new method is then applied to two challenging OED applications from chemicalengineering. Its performance compares favorably to an available existing implementation." @default.
• W2562149025 created "2017-01-06" @default.
• W2562149025 creator A5036317597 @default.
• W2562149025 date "2015-01-01" @default.
• W2562149025 modified "2023-09-25" @default.
• W2562149025 title "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations" @default.
• W2562149025 doi "https://doi.org/10.11588/heidok.00019170" @default.
• W2562149025 hasPublicationYear "2015" @default.
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