Nonlinear Programming

Fall 2013

MATP6600 / DSES6780

Note: there is now an LMS page for this course, which contains the homework solutions and the course notes. The direct links below are to pdf files on the math department web server.

Course basics:

Course outline.

Material on reserve in the library.

Scores on the homeworks and exams to date.

Exams

Homework

Solutions to completed homeworks are available on LMS.

Handwritten notes:

Note: the math department webserver is back up, so the links to the notes should work. Copies of the notes have been placed on LMS.

Introduction, including compressed sensing. (27 Aug).

Convex sets:

Convex functions

Linear programming

Optimality conditions for nonlinear programming

Duality

Algorithms

Handouts:

Linear algebra (27 Aug).
Subspaces, affine sets, convex sets, and cones (30 Aug).
Extreme points and rays, and resolution (24 Sep).
The simplex algorithm (24 Sep).
An iteration of the simplex algorithm (24 Sep).
Dimension and faces (24 Sep).
Nonlinear programming packages on NEOS. For a more detailed survey of nonlinear programming algorithms, see a paper by Leyffer and Mahajan. (26 Nov).

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