Class 8



  1. Optimality and Duality Continued...
    1. Examples of LP and convex QP duals in finite/infinite dimensions
      • Comparison of examples in Hilbert and Banach spaces, i.e. Lagrange multiplier acts using an inner-product when the image of the constraint is an inner-product space; the action is still a bilinear form when the Lagrange multiplier is in the dual of a normed space. (The dual of C[0,1] is BV[0,1]. The optimal value in Example 3 is attained by a discontinuous function in (22), but the value can be approximated as closely as desired by a continuous function. This does not contradict the fact that C[0,1] is a Banach space.)
    2. Examples of duality gaps in convex programs
    3. First and Second order optimality conditions for general NLPs
  2. Basics of Linear Programming