15.084J | Spring 2004 | Graduate

Nonlinear Programming


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

Course Info

Learning Resource Types
Lecture Videos
Lecture Notes