Convex Constraint

Convex constraints in optimization problems are central to ensuring solutions satisfy predefined conditions, a crucial aspect across diverse fields. Current research focuses on developing efficient algorithms, such as proximal gradient methods and augmented Lagrangian methods, to handle these constraints within various model architectures, including neural networks and reinforcement learning frameworks. This work addresses challenges like achieving low regret and minimal constraint violation in online settings, and guaranteeing feasibility in applications such as power flow optimization and image alignment. The resulting advancements improve the accuracy, efficiency, and reliability of solutions in numerous practical applications and theoretical analyses.