Lagrangian Multiplier

Lagrangian multipliers are mathematical tools used to solve constrained optimization problems by transforming them into unconstrained problems. Current research focuses on improving the efficiency of finding optimal Lagrangian multipliers, particularly for large-scale problems, using machine learning techniques such as graph neural networks and deep learning architectures to predict or learn these multipliers directly, bypassing traditional iterative methods. This accelerates the solution of complex optimization problems across diverse fields, from operations research (e.g., the traveling salesman problem) to engineering design (e.g., topology optimization), improving both solution speed and optimality.