Fixed Time

Fixed-time convergence in optimization algorithms focuses on designing methods that reach a solution within a predetermined time, regardless of the starting point. Current research emphasizes developing gradient-based algorithms and dynamical systems that guarantee this fixed-time convergence, even for non-convex problems, often leveraging techniques like integral sliding mode control and exploiting properties such as the Polyak-Łojasiewicz inequality. This research area is significant because it promises faster and more reliable solutions for various applications, including machine learning, robotics (e.g., human-robot collaboration), and other fields requiring efficient optimization. The resulting algorithms offer improved performance compared to traditional methods with variable convergence times.