Nonlinear Programming

Fall 2016

MATP6600 / ISYE6780

Course basics:

Course outline.

LMS. Scores on the homeworks, midterm, and final will be available on LMS. The course notes are available via LMS (as well as directly from this page), and the course version of AMPL is also available via LMS.
The score on HW2 is now available on LMS.
Aggregate scores over the first two homeworks, out of 110, are: 109 106 106 106 104 102 102 100 100 99 97 94 94 93 93 91 78 74.

Material on reserve in the library.

Exams

Homework

Handwritten notes:

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