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The following topics were substantially covered in the class:

1. Convex sets, convex cones (and the dual), convex functions. Strong
convexity.
2. Convex optimization problems :
      - definition of convex opt problem
      - inequality constrained problems; generalized inequality
      constrained problems
      - Rockafellar-Pshenichni optimality condition

3. (Lagrangian) Duality
      - how to write down the Lagrangian
      - how to find the hidden constraints
      - how to write down the dual functional
      - how to write down the dual

      - weak duality theorem
      - strong duality theorem
      - constraint qualifications (e.g. Slater condition),
      conditions that imply strong duality
      - KKT conditions

4. Steepest descent
5. Newton's method
      - how to write the Newton system for an unconstrained /
      equality constrained problem
      - damped Newton's method
      - Newton decrement

6. interior point method
      - log-barrier function : find the log-barrier function
      corresponding to an inequality constraint
      - barrier method : writing an inequality-constrained
      problem as an unconstrained problem with the new
      objective function including the barrier function


Note that, as mentioned in the class, this exam will not be
like the mid-term, where you have all the questions straight from the
assignments.
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