Lagrange Multipliers

The method of Lagrange multipliers is a classical yet powerful tool for solving constrained optimization problems. The key idea is to combine the objective function and constraints into a single structure in order to identify optimal points. It has wide applications in economics, physics, engineering, and machine learning. It is especially effective when constraints are a natural part of the problem. The Lagrange framework unifies the goals of “find the best” and “respect the rules” within the same mathematical structure.