<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations"^^ . "In this thesis we develop algorithms for the numerical solution of problems from nonlinear\r\noptimum experimental design (OED) for parameter estimation in differential–algebraic\r\nequations. These OED problems can be formulated as special types of path- and control-\r\nconstrained optimal control (OC) problems. The objective is to minimize a functional on\r\nthe covariance matrix of the model parameters that is given by first-order sensitivities of the\r\nmodel equations. Additionally, the objective is nonlinearly coupled in time, which make\r\nOED problems a challenging class of OC problems. For their numerical solution, we propose\r\na direct multiple shooting parameterization to obtain a structured nonlinear programming\r\nproblem (NLP). An augmented system of nominal and variational states for the model\r\nsensitivities is parameterized on multiple shooting intervals and the objective is decoupled\r\nby means of additional variables and constraints. In the resulting NLP, we identify several\r\nstructures that allow to evaluate derivatives at greatly reduced costs compared to a standard\r\nOC formulation.\r\nFor the solution of the block-structured NLPs, we develop a new sequential quadratic\r\nprogramming (SQP) method. Therein, partitioned quasi-Newton updates are used to approximate the block-diagonal Hessian of the Lagrangian. We analyze a model problem with\r\nindefinite, block-diagonal Hessian and prove that positive definite approximations of the\r\nindividual blocks prevent superlinear convergence. For an OED model problem, we show\r\nthat more and more negative eigenvalues appear in the Hessian as the multiple shooting grid\r\nis refined and confirm the detrimental impact of positive definite Hessian approximations.\r\nHence, we propose indefinite SR1 updates to guarantee fast local convergence. We develop\r\na filter line search globalization strategy that accepts indefinite Hessians based on a new\r\ncriterion 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 promote\r\nconvergence. For the solution of the arising sparse and nonconvex quadratic subproblems, a\r\nparametric active set method with inertia control within a Schur complement approach is\r\ndeveloped. It employs a symmetric, indefinite LBL T -factorization for the large, sparse KKT\r\nmatrix and maintains and updates QR-factors of a small and dense Schur complement.\r\nThe new methods are complemented by two C++ implementations: muse transforms an\r\nOED or OC problem instance to a structured NLP by means of direct multiple shooting.\r\nA special feature is that fully independent grids for controls, states, path constraints, and\r\nmeasurements are maintained. This provides higher flexibility to adapt the NLP formulation\r\nto 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 an\r\nimplementation of the new SQP method that uses a newly developed variant of the quadratic\r\nprogramming solver qpOASES. Numerical results are presented for a benchmark collection of\r\nOED and OC problems that show how SR1 approximations improve local convergence over\r\nBFGS. The new method is then applied to two challenging OED applications from chemical\r\nengineering. Its performance compares favorably to an available existing implementation."^^ . "2015" . . . . . . . "Dennis"^^ . "Janka"^^ . "Dennis Janka"^^ . . . . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (PDF)"^^ . . . "dissertation_janka.pdf"^^ . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (Other)"^^ . . . . . . "small.jpg"^^ . . . "Sequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations (Other)"^^ . . . . . . "indexcodes.txt"^^ . . "HTML Summary of #19170 \n\nSequential quadratic programming with indefinite Hessian approximations for nonlinear optimum experimental design for parameter estimation in differential–algebraic equations\n\n" . "text/html" . . . "510 Mathematik"@de . "510 Mathematics"@en . .