Note that there were no recitations during the weeks of the midterm exam (week 7), spring break (week 8), or Sloan Innovation Period (week 9).

1 The Basic Problem
Basic Definitions
Weirstrass Theorems
Necessary and Sufficient Conditions for Optimality
( PDF)
2 Newton’s Method
When Newton’s Method Fails
Rates of Convergence
Quadratic Forms
( PDF)
3 Method of Steepest Descent
Why this Method is Good
Why this Method is Bad
Line Search Algorithm
( PDF)
4 Separating Hyperplanes
Theorem of The Alternative (Farkas Lemma)
Necessary Conditions for Optimum of Constrained Problem
Finding Optima
( PDF)
5 When is KKT Necessary
Sufficient Conditions
Steepest Descent for Constrained Problems
( PDF)
6 Penalty/Barrier Methods
Quiz Review
( PDF)
10 Importance of Duality
Lagrangian Dual Approach
Features of The Dual
Column-Geometry Dual Approach
Weak Duality
Strong Duality
( PDF)

Course Info

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