525 Computing Project 2, Fall 2011
DMTF with Compressed Sensing:
The Past Meets the Future
Way back in the day when we all had land lines, the phone company
gured out who you were calling using a clever scheme called dual-tone multifrequency signaling (DT
525 Computing Project 2, Spring 2012
The Disputed Federalist Papers
Linear and quadratic programming can be used to solve problems in many
applications. In this project, we will apply quadratic programming to a
machine learning formulation to determine th
525 Computing Project 1, Fall 2011
Its a small world, after all
In the 1960s, Stanley Milgram conducted an experiment to determine the
diameter of the social network of the united states. Beginning with a few
people in Kansas and Nebraska, participants we
CS 525 - Fall 2011 - Homework 9
For extra credit
assigned 11/30/11, due 12/8/11
1. Do Exercise 7-1-3
2. Do Exercise 7-2-2
3. (a) Write down the KKT conditions for the problem
minimize x2 + x2 + x2
3
2
1
subject to x1 + x2 + x3 1
x1 x2 x3 1
x1 + x 2 x3 1
x
CS 525 - Fall 2011 - Homework 8
assigned 11/16/11 - due 11/30/11
1. Which of the following sets are convex?
(a) cfw_x R : x2 = 1.
(b) cfw_x R : x2 1.
(c) cfw_x R : x2 1.
2. Let A be an m n matrix. Verify that the set
cfw_x Rn : Ax = b , x 0
is a convex se
CS 525 - Fall 2011 - Homework 7
assigned 11/9/11 - due 11/16/11
1. Consider the standard min-cost network ow problem (5.15) from page
145 in the book. Suppose = 0 and u = . Prove that there exists
an optimal solution with at most |N | non-zero edge ows.
2
CS 525 - Fall 2011 - Homework 6
assigned 10/19/11 - due 11/7/11
1. Do Exercise 4-8-1.
2. Do Exercise 4-9-1.
3. Do Exercise 4-9-3.
4. Do Exercise 5-1-2.
5. Do Exercise 5-1-5.
Hard copy to be submitted in class on the due date. No late homework accepted.
CS 525 - Fall 2011 - Homework 5
assigned 10/12/11 - due 10/19/11
1. Do Exercise 4-5-2.
2. Do Exercise 4-6-4.
3. Consider the LP:
minimize cT x
n
subject to
i=1 xi = 1
x0
(a) Write down the dual problem
(b) Write down the KKT conditions.
(c) Find an optima
CS 525 - Fall 2011 - Homework 4
assigned 10/5/11 - due 10/12/11
1. Do Exercise 3-4-2.
2. Do Exercise 3-4-3.
3. Solve the problem in Exercise 4-2-2 by adding dual labels to the tableau
and applying Phase I and Phase II in the usual way. (Hint: If you need
CS 525 - Fall 2011 - Homework 3
assigned 9/21/11 - due 9/28/11
Hand in an annotated diary le, constructed as outlined in the MATLAB
Setup handout and in Homework 1.
1. The
norm of a vector z is given by
z
The
1
= max |zi | .
1im
norm of a vector is given
CS 525 - Fall 2011 - Homework 2
assigned 9/14/11 - due 9/21/11
Hand in an annotated diary le, constructed as outlined in the MATLAB
Setup handout and in Homework 1. Your diary should contain a record of
your session and should look something like the foll
CS 525 - Fall 2011 - Homework 1
For practice only (not for submission)
assigned 9/7/11
The data for this problem, namely
135
2 1 3
126
,
, B = 4 1 8 , C =
A=
10 1
345
111
1
1
3
2
1
4
1
x = , y = , z = 2 , = 3,
0
5
1
2
2
6
3
can be loaded within MATLAB fro