EE 150 - Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 2011-2012
Homework Set #5
Due on Friday, May 11 at 1 PM in 110 Moore.
1. (10 points) (Adapted from CO-BV, Exercise 4.20) (Power assignm
ECE 788 - Optimization for wireless networks
Midterm
Please provide clear and complete answers.
PART I: Questions - Provide a proof or a convincing example to answer the following:
Q.1. (1 point) Is cfw_(x, t) Rn R| kxk2 t a convex set?
Sol.: No. It is en
EE 150 - Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 2011-2012
Homework Set #1
Due on Thursday, April 12 in class.
1. (10 points) Send a brief message with your name in full to the course
ECE 788 - Optimization for wireless networks
Final
Please provide clear and complete answers.
1. (4 points) Consider the optimization problems P1, P2, P3 and P4 below, where fo (x) is
the cost function and f1 (x) denes the inequality constraint (i.e., the
Linear Programming Exercises
Lieven Vandenberghe
Electrical Engineering Department
University of California, Los Angeles
Fall Quarter 2013-2014
1
Hyperplanes and halfspaces
Exercise 1. When does one halfspace contain another? Give conditions under which
c
EE 150 - Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 2011-2012
Homework Set #4
Due on Thursday, May 3 in class.
1. (10 points) (Adapted from CO-BV, Exercise 3.49) (Log-concave functions:)
EE 150 - Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 2011-2012
Homework Set #3
Due on Thursday, April 26 in class.
1. (10 points) (Adapted from CO-BV, Exercise 2.9) (Voronoi sets and polyh
EE 150 - Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 2011-2012
Homework Set #2
Due on Thursday, April 19 in class.
1. (10 points) (Existence of Moore-Penrose pseudoinverse:) Recall that if
Chapter 2
Multi-objective Optimization
Abstract In this chapter, we introduce multi-objective optimization, and recall some
of the most relevant research articles that have appeared in the international literature related to these topics. The presented st
The 2013 International Conference on Advanced Technologies for Communications (ATC'13)
Multiuser Scheduling in Two-Way Relay Networks
Department
Vien Nguyen-Duy-Nhat , Hung Nguyen-Le , Chien Tang-Tan
of Electronics and Telecommunications Engineering, The
EE364a Review
EE364a Review Session 2
session outline:
dual cones
convex functions
conjugate function
1
Dual cones
for a cone K, the dual cone is K = cfw_y | y T x 0 for all x K
y K if and only if the halfspace cfw_z | y T z 0 contains K
K
90
90
K
EE36
The CVX Users Guide
Release 2.0 (beta)
Michael C. Grant, Stephen P. Boyd
CVX Research, Inc.
November 03, 2012
CONTENTS
1
2
3
4
5
Introduction
1.1 What is CVX? . . . . . . . . . . . . . . .
1.2 What is disciplined convex programming?
1.3 What CVX is not .
Convex Optimization Boyd & Vandenberghe
2. Convex sets
ane and convex sets
some important examples
operations that preserve convexity
generalized inequalities
separating and supporting hyperplanes
dual cones and generalized inequalities
21
Ane set
l
EE364a, Winter 200708
Prof. S. Boyd
EE364a Homework 3 additional problems
1. Optimal activity levels. Solve the optimal activity level problem described in exercise
4.17 in Convex Optimization, for the instance with problem data
A=
1
0
0
2
1
2
0
3
1
0
0
3
EE571 Homework 7
Out Nov 17 2014
Due in Class Dec 5 2014
Do the following problems from the book.
6.1
6.7
7.1
7.3
A3.20
The data file for A3.20 can be found in the data file directory on the textbook page.
A12.6
A13.2
EE571 Homework 4
Out Oct 8 2014
Due in Class Oct 15 2014
Do the following problems from the book.
4.5
4.8 (a-d)
4.11
4.16
4.17
4.29
http:/www.seas.ucla.edu/~vandenbe/ee236a/homework/problems.pdf
EE571 Homework 1
Out Sept 4 2014
Due in Class Sept 15 2014
Do the following problems from the book.
2.1
2.2
2.5
2.8
2.10
2.12
http:/arni.epfl.ch/_media/courses/convexoptimization2012/solutions1.pdf
EE571 Homework 2
Out Sept 17 2014
Due in Class Sept 24 2013
Do the following problems from the book.
2.27
2.28
2.32
3.15
3.16 (b-e)
3.18 (a)
3.20 (c)
http:/see.stanford.edu/materials/lsocoee364a/review1_single.pdf