The global optimization problem and the contribution of Prof. Angelo Miele: the Green' s theorem approach

摘要

Optimization of aerospace trajectories requires intensive numerical work and educated guesses to start iterative routines whose convergence to a result is not garanteed. For this reason once a solution has been achieved, it is often overlooked the question whether the solution is just a local optimum (close to the initial guess) or a global optimum. There are few tools to support the search of globally optimal solutions: Prof. Miele introduced a method based on the Green's theorem that allows to find locally optimal solutions and distinguish the global optimum among them . This method, initially applied to aeronautics, was proved effective also in the context of space systems and in many other engineering disciplines. Some results concerning global optimization are here presented pointing out that the reduction of dimension of the space of admissible solutions is the key to solve optimization problems and find the global optimum.