Yutong Zhang, Wentao Zhang, Lulu Zhang, Hanshen Li, Wentao Mo
Amid the exponential growth of streaming data and rising demands for real-time decision-making, Online Convex Optimization (OCO) has emerged as a foundational framework for sequential data processing in dynamic environments. This survey presents a systematic review of recent evolutionary and adaptive OCO strategies, offering a detailed taxonomy that classifies algorithms according to their constraint-handling mechanisms and environmental feedback. The analysis first examines Constrained OCO, elucidating the trade-offs between computational efficiency and theoretical guarantees across projection-based methods, projection-free Frank–Wolfe variants, and general convex optimization approaches. It then explores the Unconstrained OCO landscape, emphasizing the shift from parameter-dependent methods to fully adaptive, parameter-free algorithms capable of handling unknown comparator norms and gradient scales. Furthermore, the study synthesizes state-of-the-art applications in power systems, network communication, and quantitative finance, bridging theoretical OCO models with robust engineering solutions. The paper concludes by outlining critical open challenges and future research directions, such as the integration of OCO with deep learning, non-convex optimization, and robustness against adversarial corruptions in data-intensive scenarios.