A study on Optimization Methods in Celestial Mechanics

This text explores advanced methods for solving the N-body problem, particularly through variational approaches and optimization techniques. The focus is on finding critical points of the action functional, which correspond to potential orbits. Various optimization strategies, including trust region methods, constrained optimization, and metaheuristic meth- ods, are discussed for their effectiveness in identifying minima, saddle points, and other critical points. The text emphasizes the importance of choosing efficient algorithms and the challenges in distinguishing between local and global solutions in nonlinear optimization problems. The goal is to gather a wide range of solutions to gain deeper insights into the system’s behaviour and uncover new properties.