Nonlinear Programming
Fall 2015
MATP6600 / ISYE6780
Course basics:
Course outline.
LMS.
Scores on the homeworks and midterm will be available on LMS.
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 26).
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