1. Optimality conditions constrained optimisation
for
constrained optimisation

2. Recall: Optimisation conditions for unconstrained problem with one variable function

5. Recall: Optimisation conditions for unconstrained problem with several variables function

13. Lagrangean multipliers

14. Lagrangean multipliers

15. Optimisation conditions for constrained problem

30. First order Karush-Kuhn-Tucker (KKT) optimality conditions

33. Sufficiency of the K-K-T conditions

34. Sufficiency of the K-K-T conditions

35. Sufficiency of the K-K-T conditions

41. Necessity of the K-K-T conditions

128. Kuhn-Tucker constraints qualification

142. K-K-T condition for linear programming

143. K-K-T condition for linear programming

144. K-K-T condition for linear programming

145. K-K-T condition for linear programming