MATHEMATICAL OPTIMIZATION OF ARTIFICIAL INTELLIGENCE ALGORITHMS

Artificial intelligence (AI) algorithms, particularly those underlying machine learning and deep learning models, fundamentally rely on mathematical optimization to achieve accurate and efficient performance. This article reviews the mathematical foundations and modern techniques used to optimize AI algorithms, with emphasis on gradient-based methods, second-order optimization techniques, stochastic and evolutionary approaches, and hybrid optimization strategies. This review aims to provide researchers and practitioners with a structured understanding of the mathematical optimization landscape underlying contemporary AI systems and to highlight emerging directions for further research.