Strongly Convex

Strongly convex functions, a class of convex functions with a unique minimum, are central to optimization problems across numerous fields. Current research focuses on developing efficient algorithms, such as stochastic gradient methods and their variants (e.g., optimistic gradient, variance-reduced methods), to solve strongly convex problems, particularly in the context of minimax optimization and distributed settings. These advancements improve the speed and scalability of solving complex optimization problems arising in machine learning, including applications like adversarial training and federated learning, leading to more efficient and robust model training. The development of tighter theoretical bounds on algorithm convergence rates and generalization error is also a key area of investigation.