An Inverse-Based Algorithm for Global Optimization

Global function optimization is a vital area of applied mathematics, and it has numerous applications across fields such as machine learning, economics, and engineering design. Despite the extensive array of gradient-based and gradient-free optimization algorithms that leverage direct search strategies, the inverse approach to address optimization problems remains relatively unexplored. This paper focuses on the development of an inverse-based algorithms designed to solve global optimization problems that relies on the sequential resolution of inverse problems. The study involved executing computational experiments and comparing the proposed algorithm to existing methods to evaluate its effectiveness in optimizing the functions analyzed. In particular, the experiments focused on the global optimization of test functions and the training of neural networks. The obtained results can be used in further research and practical applications in diverse fields, including machine learning and the optimization of complex systems.