# Introduction to Optimization

## MATP6600 / ISYE6780

### Handwritten notes from Nonlinear Programming:

Introduction, including compressed sensing. (Lecture 1).

Convex sets:

Convex functions

Linear programming

Optimality conditions for nonlinear programming

Duality

Algorithms

### Handouts:

Linear algebra (Lecture 1).
Subspaces, affine sets, convex sets, and cones (Lecture 2).
2 theorems on convex functions (Lecture 4).
Differentiable functions (Lecture 4).
Hessians of smooth convex functions (Lecture 5).
Normal cones (Lecture 7).
Extreme points and rays, and resolution (Lecture 8).
Dimension and faces (Lecture 8).
The simplex algorithm (Lecture 9).
An iteration of the simplex algorithm (Lecture 9).
An example of solving a Lagrangian dual problem. (Lecture 17).
Nonlinear programming packages on NEOS. For a more detailed survey of nonlinear programming algorithms, see a paper by Leyffer and Mahajan. (Lecture 24).

### Resources:

Convex Optimization by Boyd and Vandenberghe.
A nonlinear programming FAQ, including links to collections of test problems.
The NEOS Server has some nonlinear programming packages available.
An introduction to the conjugate gradient method without the agonizing pain, by Jonathan Shewchuk.
A survey of pattern search and related methods by Charles Audet.
Issue 78 of the Mathematical Optimization Society newsletter Optima, discussing smoothing methods.
Slides on the alternating direction method of multipliers, by Stephen Boyd. Here's the underlying survey paper.
John Mitchell's homepage | Dept of Mathematical Sciences Course Materials