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
Eigenvectors/Eigenvalues/Decompositions | (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) |
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