Optimization in Communications Engineering
WS 2015/16
1
2. Convex Functions
Problem 2.1 Definition of Convexity/Concavity
Determine whether the following functions are convex and/or concave:
a)
fA (x)
Optimization in Communications Engineering
WS 2015/16
5. Optimality Conditions
Problem 5.1 Least Squares Problem
Consider the optimization problem
min kAx bk22 ,
x
where x Rn , A Rmn , and b Rm .
a)
G
Optimization in Communications Engineering
WS 2015/16
1
3. Extreme Points, Extreme Directions, and Polyhedral Sets
Problem 3.1 Standard Forms of Polyhedral Sets
Consider the following two standard for
Optimization in Communications Engineering
WS 2015/16
1
1. Convex Sets
Problem 1.1 Linear Spaces, Affine Sets, Cones, and Convex Sets
For each of the following sets, determine if it is a linear space,
Optimization in Communications Engineering
WS 2015/16
1
4. Linear Programming and the Simplex Method
Problem 4.1 Simplex Method
Consider the linear program
min cT x s.t. Ax = b, x 0,
(4.1)
where A = [