Class 15



  1. Theory of Constrained Optimization, Chap. 12, cont...
    (with basic convex analysis added)
    1. Basic Hyperplane Separation Theorem
    2. Lemma: K is a closed convex cone if and only K=K++ (for derivation of Farkas' Lemma)
    3. Linearizing Cone, Cone of Gradients, Weakest Constraint Qualification, Karush-Kuhn-Tucker conditions
    4. Generalized Convex Program (perturbation function)
    5. Lagrange Multiplier Theorem (with proof) of Generalized Convex Program
    6. Application of convex dual to the Control Theory Example.