# 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)**