This research tackles fundamental challenges in optimization by developing advanced adaptive fast gradient methods for solving saddle point and constrained optimization problems. A new approach termed Adaptive Fast Gradient Method with Restart (restart-AdaFGM) is introduced to enhance both computational performance and theoretical convergence guarantees. Theoretical analysis confirms that this method achieves optimal convergence rates, addressing limitations in existing methods. Extensive numerical experiments demonstrate the efficiency of restart-AdaFGM compared to the conventional Adaptive Fast Gradient Method (AdaFGM). The proposed method excels particularly in handling non-smooth problems with functional constraints. Furthermore, comparative studies highlight its robustness and efficiency in a wide range of optimization scenarios. These findings underscore the practical value of restart-AdaFGM in improving execution times and solving complex problems more effectively. By addressing key limitations of current methods, restart-AdaFGM represents a significant contribution to the development of advanced optimization techniques and their application in challenging problem domains.