Solutions to Homework 3
EL-GY 6223 System Optimization Methods
Fall 2015, New York University
Problem 1 (Problem involving l1 and l norms). [BV] Problem 4.11 (a) and (b)
Problem 2 (Network flow problem). [BV] Problem 4.12
Problem 3 (Power assignment in a

Solutions to Homework 5
EL 6223 System Optimization Methods
Fall 2015, New York University
November 30, 2015
Problem 1. Minimize the cost function
Z
x1
J=
0
p
1 + (y 0 )2
dx,
y
with y(0) = 0, and the end point (x1 , y1 ) is constrained on the given curve

Solutions to Homework 6
EL-GY 6233 System Optimization Methods
Fall 2015, New York University
Problem 1. A gambler enters a game whereby he may, at time k, stake any amount uk 0 that does not
exceed his current fortune xk (defined to be his initial capita

Solutions to Homework 1
EL-GY 6223 System Optimization Methods
Fall 2015, New York University
Problem 1
Problem 2
Problem 4
Problem 3
(1) The eigenvalues are 0, 2, 3. The eigenvectors are (2, -1, 0)T, (-10, 3, 1)T, and (1, 0,
0)T, respectively.
(2) The de

Solutions to Homework 2
EL-GY 6223 System Optimization Methods
Fall 2015, New York University
Problem 1 (Convex Functions). [BV] Problem 3.23(b)
Problem 2 (Convex Functions). [BV] Problem 3.49
(a)
(b)
(c)
(d)
Problem 3 (Quadratic Programming). [BV] Proble