Class 5



  1. Theory of Constrained Optimization, cont...
    (with basic convex analysis)
    1. Basic Hyperplane Separation Theorem (with proof)
    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. Lemma: K is a ccc iff K=K++ and proof using separation theorem
    5. derivation of Farkas' Lemma (using above lemma); extensions/failure of Farkas' lemma