C&O 463/663: Convex Optimization and Analysis
(Fall 2012)
Assignment 1
H. Wolkowicz
Handed out Tues. 2012-Sept-18
Due: Thurs., 2012-Sept-27, 11:30AM (before class),
1
Convex Sets
1. Let S Rn .
(a) Show that the set S Rn is convex if and only if its inters

C&O 463/663: Convex Optimization and Analysis
(Fall 2012)
Assignment 6
H. Wolkowicz
Handed out Thurs., 2012-Nov-15
Due: Thur., 2012-Nov-29, 11:30AM (before class),
1. Let Si , i = 1, . . . , n be nonempty sets in Rm ; let S := n Si ; and let x conv S. Sho

C&O 463/663: Convex Optimization and Analysis
(Fall 2012)
Assignment 5
H. Wolkowicz
Handed out Thurs., 2012-Nov-1
Due: Thur., 2012-Nov-15, 11:30AM (before class), (Thanks Ahmad for solutions.)
1. Show that the function (x, t) tg(x/t), for t > 0, x Rn is c

C&O 463/663: Convex Optimization and Analysis
(Fall 2012)
Assignment 3
H. Wolkowicz
Handed out Tues., 2012-Oct-9
Due: Thurs., 2012-Oct-18, 11:30AM (before class),
1. Let C be a closed, convex, nonempty subset of Rn . Show that C has an extreme point
if, a

EE364, Spring 2005-06
Prof. S. Boyd
EE364 Homework 7 additional problems
1. State and solve the optimality conditions for the problem
"
X1 X2
minimize log det
X2T X3
subject to Tr X1 =
Tr X2 =
Tr X3 = .
#1
The optimization variable is
X=
"
X1 X2
X2T X