Assess learners' ability to apply convex optimization and KKT conditions to derive and solve constrained portfolio optimization problems (e.g., mean–variance quadratic programs with budget, box, and no-short constraints). Tasks include forming the Lagrangian, deriving KKT optimality conditions, solving for optimal weights analytically or via quadratic programming, verifying primal/dual feasibility and complementary slackness, and interpreting dual variables for sensitivity analysis.