An Effective of Numerical Global Optimization Framework For ODE-Constrained Problems

Abstract

This paper presents an innovative framework for the global numerical optimization of non-convex ordinary differential equation (ODE) constrained problems, which pose a challenge due to the presence of multiple local optima. The framework is based on convex relaxation techniques and a deterministic spatial Branch and Bound (BB) algorithm. The algorithm employs adaptive branching strategies and precisely updates the upper and lower bounds using sub- and super-function concepts, ensuring a reliable and efficient convergence to the global optimum. Numerical case studies have proven the effectiveness of this framework in overcoming the limitations of current methods.