A simulation-based approach for solving optimisation problems with ODE-type steady state constraints

TL;DR

This paper introduces a simulation-based optimization method for problems constrained by steady states of ODEs, leveraging local geometry and stability without needing manifold parameterization, showing improved convergence in examples.

Contribution

It presents a novel simulation-based approach tailored to ODE-constrained optimization that exploits local geometry and stability, with proven local convergence.

Findings

Better convergence properties than existing methods

Higher number of converged starts per time

Effective in biological and chemical process models

Abstract

Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article proposes a simple simulation-based approach for solving optimisation problems with steady state constraints relying on an ODE. This simulation-based optimisation method is tailored to the problem structure and exploits the local geometry of the steady state manifold and its stability properties. A parameterisation of the steady state manifold is not required. We prove local convergence of the method for locally strictly convex objective functions. Effciency and reliability of the proposed method are demonstrated in two examples. The proposed method demonstrated better convergence properties than existing general purpose methods and a significantly higher number of converged starts per time.