Coupled Linear Constraint

Coupled linear constraints pose a significant challenge in optimization problems arising across diverse fields, from machine learning to control systems. Current research focuses on developing efficient first-order and zeroth-order algorithms, including primal-dual methods and alternating direction methods of multipliers (ADMM), to solve these problems, particularly within the contexts of bilevel optimization and nonconvex minimax problems. These advancements enable the solution of complex optimization tasks with coupled constraints, improving the performance of applications such as hyperparameter tuning and distributed model predictive control. The development of robust and scalable algorithms for handling coupled constraints is crucial for advancing these and other application areas.