A continuation method for the efficient solution of parametric optimization problems in kinetic model reduction

Abstract

Model reduction methods often aim at an identification of slow invariant manifolds in the state space of dynamical systems modeled by ordinary differential equations. We present a predictor corrector method for a fast solution of an optimization problem the solution of which is supposed to approximate points on slow invariant manifolds. The corrector method is either an interior point method or a generalized Gauss--Newton method. The predictor is an Euler prediction based on the parameter sensitivities of the optimization problem. The benefit of a step size strategy in the predictor corrector scheme is shown for an example.

References in corpus (1)

• Constructive Methods of Invariant Manifolds for Kinetic Problems

Cited by in corpus (5)

• An optimization approach to kinetic model reduction for combustion chemistry
• A Numerical Slow Manifold Approach to Model Reduction for Optimal Control of Multiple Time Scale ODE
• Towards differential geometric characterization of slow invariant manifolds in extended state space: Sectional Curvature and Flow Invariance
• Covariant geometric characterization of slow invariant manifolds: New concepts and viewpoints
• Considering Slow Manifold Based Model Reduction for Multiscale Chemical Optimal Control Problems