Active constraint
A constraint that binds at the solution. Example: w_i = 0.10 when the max weight is 10%.
Reference 0004
KKT and Dual Variables
A compact interpretation guide for constrained optimum conditions.
Inactive constraint
A constraint with slack. Example: w_i = 0.04 when the max weight is 10%.
Dual variable
A shadow price attached to a constraint. It estimates how much the optimal value changes if that constraint is relaxed slightly.
Complementary slackness
For inequality constraints, either the constraint binds or its dual variable is zero.
Stationarity
At the optimum, the objective gradient is balanced by the gradients of active constraints.
Economic reading
A large dual on a portfolio cap means the optimizer badly wants more room there, according to the model.
Convex KKT checklist
At the optimum, check: + primal feasibility: constraints are satisfied + dual feasibility: inequality duals have the right sign + complementary slackness: inactive constraints have zero duals + stationarity: no feasible first-order improvement remains
Use this page while reading Lesson 0004.