Karush-Kuhn-Tucker theorem

The Karush-Kuhn-Tucker (KKT) theorem provides conditions to find the best solution for optimization problems with constraints. Imagine trying to maximize or minimize a function while satisfying certain rules or limits. The KKT conditions help identify points where the solution balances the goal and the constraints, revealing optimal solutions. They do this by introducing additional factors called Lagrange multipliers that account for constraints, ensuring that at the optimum, the function's slope aligns with the constraints' boundaries. This theorem is fundamental in fields like economics, engineering, and machine learning for solving complex optimization tasks efficiently.