Lagrangian Relaxation

Lagrangian relaxation is a mathematical technique used to solve constrained optimization problems by relaxing constraints and incorporating them into the objective function via Lagrange multipliers. Current research focuses on improving the efficiency and applicability of Lagrangian relaxation, particularly within machine learning contexts, using methods like augmented Lagrangian methods, and incorporating it into deep learning architectures (e.g., neural networks, reinforcement learning) for various applications. This approach is proving valuable in diverse fields, including power plant control, solving combinatorial optimization problems (like the traveling salesman problem), and accelerating optimization in federated learning and optimal transport calculations.