• The Best Way to Learn: Taking a Test? ... so... please thank us for giving you an exam. (detailed article and summary)
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    The following topics were substantially covered in the class:
    
    1.  (definitions, geometry, intersections, examples of:)
         Convex sets 
         convex cones (and the dual/polar), separation theorems 
         convex functions (directional derivatives, characterizations, epigraph)
         strong convexity.
    
    
    2. Convex optimization problems :
          - definition of convex opt problem
          - inequality constrained problems; generalized inequality
          constrained problems
          - Rockafellar-Pshenichni optimality condition
    
    3. Optimality (KKT) and (Lagrangian/weak/strong) 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/when needed),
          conditions that imply strong duality
          - KKT conditions (difference between sufficiency and necessity)
    
    4. Steepest descent algorithm for function minimization
           -  deriving the steepest descent direction
           -  steplength decisions
    
    5. Newton's method
          - Newton's method for system of nonlinear equations
          - how to write the Newton system for an unconstrained /
          equality constrained problem
          - damped Newton's method
          - Newton decrement
          - importance/role of quadratic functions
    
    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
          - log-barrier problem applied to LP, and derivation of modern primal-dual
            interior point methods for LP
    
    
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