Optimization and Computational Linear Algebra

New York University - Fall 2017

Class is held in 60FA 110, Tue 4:55-6:35pm

Lecture 1 (Tuesday, September 5): Introduction, solving linear equations

Lecture 2 (Tuesday, September 12): Vector spaces and orthogonality

Lecture 3 (Tuesday, September 19): Least squares approximation, Gram-Schmidt, determinants, eigenvalues and eigenvectors

Lecture 4 (Tuesday, September 26): Markov, symmetric, positive definite matrices, singular value decomposition (SVD)

Lecture 5 (Tuesday, October 3): Numerical computation, norms and condition numbers, iterative methods

Lecture 6 (Tuesday, October 10): Covariance matrices, weighted least squares

Midterm (Tuesday, October 17): in class

Lecture 7 (Tuesday, October 24): Introduction to optimization
Linear programs (LP), integer programs (IP), non-linear programs (NLP),

Lecture 8 (Tuesday, October 31): Solving linear programs. Simplex algorithm.

Lecture 9 (Tuesday, November 7): Duality theory. Solving integer programs.

Lecture 10 (Tuesday, November 14): Convexity, optimality.

Lecture 11 (Tuesday, November 21): Quadratic programs, regularization, sparsity.

Thanksgiving recess (Wednesday-Sunday, November 22-26)

Lecture 12 (Tuesday, November 28): Convex optimization hierarchy, gradient descent.
LP ⊂ QP ⊂ SOCP ⊂ SDP ⊂ Conic programs.

Lecture 13 (Tuesday, December 5): Iterative optimization algorithms.

Legislative Day (Tuesday, December 12): Classes will meet according to a Monday schedule

Last day of Fall 2017 classes (Friday, December 15)

Final exam (Tuesday, December 19)