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 three homeworks, out of 170, are: 163 160 157 156 154 154 152 151 151 150 144 142 141 141 136 135 131 122.

Material on reserve in the library.



Handwritten notes:

Introduction, including compressed sensing. (Lecture 1).

Convex sets:

Convex functions

Linear programming

Optimality conditions for nonlinear programming




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).


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