Constrained Optimization When to Use Use this skill when working on constrained-optimization problems in optimization. Decision Tree 1. Constraint Classification - Equality: h(x) = 0 - Inequality: g(x) <= 0 - Bounds: l <= x <= u 2. Lagrangian Method (Equality Constraints) - L(x, lambda) = f(x) + sum lambda j h j(x) - Solve: grad x L = 0 and h(x) = 0 - 3. KKT Conditions (Inequality Constraints) - Extend Lagrangian with mu i for g i(x) <= 0 - Complementary slackness: mu i g i(x) = 0 - 4. Penalty and Barrier Methods - Penalty: add P(x) = rho sum max(0, g i(x))^2 - Barrier: add B(x) = -sum log(-g…