ENEE 662
ASSIGNMENT 3
SOLUTION
Required problems:
(3.2) The first function could be quasiconvex because the sublevel sets appear to be convex. It is definitely
not concave or quasiconcave because the superlevel sets are not convex. It is also not convex,

ENEE 662
ASSIGNMENT 6
SOLUTION
Textbook required problems:
(4.29) u = cT x is a normal random variable with mean cT x and variance kR1/2 xk22 . Thus,
u cT x
u cT x
cT x
cT x
N (0, 1) = P[u ] = P
=1
kR1/2 xk2
kR1/2 xk2
kR1/2 xk2
kR1/2 xk2
where is the c

ENEE 662
ASSIGNMENT 4
SOLUTION
Textbook required problems:
(4.6) This problem can be proved by contradiction. Suppose problem (4.66) has one optimal solution x
with h(x ) < 0. Since h(x) is monotonically decreasing with respect to xr , there must exist x

ENEE 662
ASSIGNMENT 10
Due Friday 2 December 2016
(*) Do the following problems from the book:
5.18 Separating hyperplanes between polyhedra; a few ways to do it, with or without
theorem of alternatives.
5.25 We discussed saddle-point and biconjugate appr

ENEE 662
ASSIGNMENT 9
Due Thursday 10 November 2016
(*) Do the following problems from the book:
5.26 KKT without Slater.
5.27 Solving a constrained least-squares problem via optimality conditions.
5.39 SDP relaxations of partitioning problem.
(*) Do the

ENEE 662
ASSIGNMENT 2
Due Thursday 15 September 2016
(*) Do the following problems from the book:
2.15(a,b,e-g) These just give more practice figuring out what is or isnt convex, this
time asking these questions with probability distributions. They have m

ENEE 662
ASSIGNMENT 3
Due Thursday 22 September 2016
(*) Do the following problems from the book:
3.1 Deriving basic conditions on derivatives.
3.14 Saddle points.
3.16(a,b,d) Determining convex, concave, quasiconvex, quasiconcave.
3.18(a) Function of mat

ENEE 662
ASSIGNMENT 8
Due Thursday 3 November 2016
(*) Do the following problems from the book:
5.14 Relation between penalty method and dual bounds. You can also think of (x, )
as an alternate Lagrangian, and think about whether the four main properties

ENEE 662
ASSIGNMENT 6
Due Thursday 13 October 2016
(*) Do the following problems from the book:
4.29 Maximizing probability of satisfying an inequality.
4.30 Basic GP setup.
4.33 (Express each one either as a convex optimization problem, or as a GP in sta

ENEE 662
ASSIGNMENT 5
Due Thursday 6 October 2016
(*) Do the following problems from the book:
4.6 Convex but non-affine equality constraints.
4.7(a,b)
4.16 Minimizing fuel use as an LP.
There is a solution where you get around 4N constraints. While this

ENEE 662
ASSIGNMENT 4
Due Thursday 29 September 2016
(*) Do the following problems from the book:
3.2 Level sets.
3.36(a,b,d) Conjugate functions.
3.43 First-order condition for quasiconvexity.
3.39(d) This involves studying the conjugate of the conjugate

ENEE 662
ASSIGNMENT 1
Due Thursday 8 September 2016
(*) Do the following problems from the book:
2.1, 2.2, 2.3 These develop equivalent conditions for convexity which are good to
have in your toolbox when you need to determine and demonstrate if sets are