Optimization Methods in Signal Processing and Communication
ELECTRICAL ee5121

Spring 2016
EE5121: Optimization Methods
HW #3: Convex Sets
Exercise 1. (Alternate ways of checking for convexity) One way to check for the convexity
of a given set is by verifying its definition, i.e., for every pair of points in the set, the line
segment joining th
Optimization Methods in Signal Processing and Communication
ELECTRICAL ee5121

Spring 2016
EE5121: Optimization Methods
HW #6: Duality for Convex Programming
Exercise 1. Solve the following exercises from Boyd:
i. 4.47
ii. 5.11
iii. 5.19 a, b
iv. 5.39
v. 5.41
Exercise 2. [Eigenvalue optimization via SDP] Consider the affine map A : Rd S m
defin
Optimization Methods in Signal Processing and Communication
ELECTRICAL ee5121

Spring 2016
EE5121: Optimization Methods
HW #5: Convex functions and optimization
1. (Boyd) 3.6, 3.7, 3.20
2. (Boyd) 4.8, 4.12, 4.14,4.17, 4.20
3. (Boyd) 5.4, 5.5, 5.7 (a and b), 5.13, 5.17,
4. Pose the following problem as an LP
min
maxi=1,.,m aTi x + bi
, such that
Optimization Methods in Signal Processing and Communication
ELECTRICAL ee5121

Spring 2016
EE5121: Optimization Methods
HW #2: Topology and Linear Algebra
1
Sequences
Exercise 1. In this problem, we will review two important numbers related to sequences lim inf
and lim sup which are defined as follows.
lim inf xn = supcfw_infcfw_xm : m > n : n
Optimization Methods in Signal Processing and Communication
ELECTRICAL ee5121

Spring 2016
EE5121: Optimization Methods
HW #4: Seperation, Cones
Exercise 1. (Distances between sets and separation: Please look at standard textbooks for help
with the proofs.) The distance between a point x and a set A is defined as
dis(x, A) = infcfw_kx yk, y A.