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.
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