Augmented Lagrangian method

The Augmented Lagrangian method is a technique used to solve complex optimization problems with constraints. It combines the original problem with additional terms that penalize violations of these constraints, improving stability and convergence. By iteratively adjusting these penalty factors and Lagrange multipliers, the method effectively guides the solution toward satisfying both the goal and the constraints simultaneously. It’s commonly used in fields like engineering and machine learning to find optimal solutions when straightforward methods struggle with constraints.