Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #1  Solutions
1. This is selfexplanatory.
2. (a) Clearly the inequality holds if a = 0 or b = 0. Furthermore,
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #2  Solutions
1. Recall that A = UV and B = V# U .
1) (AA# A = A)
Note that it is trivial to show that # = . Us
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #3  Solutions
1. (a) Note that x is closer to x0 than to x in the Euclidean norm sense if and only if we
have t
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #4  Solutions
1. (a) We have
ex
1 + ex
log(f (x) = log
= x log(1 + ex ) .
The rst term is linear and hence conc
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #5  Solutions
1. The rst thing to note is that maximizing the minimum SINR is equivalent to minimizing
the maxi
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #6  Solutions
1. (a) The feasible set is the interval [2, 4]. The (unique) optimal point or solution is x = 2,
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #7  Solutions
1. First note that we can express f (t) as
f (t) = c(t)T x ,
where we have
1
2
c(t)
cos
2 (1) t
T
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE 150  Applications of Convex Optimization in Signal Processing and Communications
Dr. Andre Tkacenko, JPL
Third Term 20112012
Homework Set #8  Solutions
1. For all parts to this problem, we will use the fact that HR (f ) can be expressed as
HR (f ) =
Applications of Convex Optimization in Signal Processing and Communications
EE 150

Spring 2011
EE/ACM 150  Applications of Convex Optimization
in Signal Processing and Communications
Lecture 1
Andre Tkacenko
Signal Processing Research Group
Jet Propulsion Laboratory
April 3, 2012
Andre Tkacenko (JPL)
EE/ACM 150  Lecture 1
April 3, 2012
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