to ODE (CVODES and IDAS) and NLP (IPOPT, SNOPT, BLOCKSQP) solvers. CasADi is a symbolic framework for automatic differentiation and numerical optimization with interfaces e.g.
#Nonmem 3 new residual variability models eta on sigma software#
The algorithm is implemented as a prototype in the software CasADi. The resulting Hessian matrix contains residual-dependent terms, which can drive the iterative optimization procedure into solutions with undesired properties, such as solutions which are strongly influenced by large residual terms in the Hessian matrix.įor this reason, we propose a GN algorithm for the first-order (FO) and first-order conditional estimation (FOCE) approximation of parameter estimation problems for nonlinear mixed-effects models. In NONMEM, the individual parameters ETA are estimated by a GN algorithm, whereas the population parameters THETA, OMEGA and SIGMA are estimated by solving an optimization problem using a variable metric method (QN Method ).
Objectives: Solving (nonlinear) least squares problems (LS problems) with a Gauss-Newton (GN) algorithm is a state-of-the-art approach and the algorithm's benefits are mathematically proven, since GN algorithms provide reliable estimates, not affected by residuals compared to Quasi-Newton (QN) and Newton algorithms. (1) Institute of Mathematical Optimization, Faculty of Mathematics, Otto-von-Guericke University Magdeburg, Germany Gauss-Newton algorithm for parameter estimation of nonlinear mixed-effects models
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