Solutions for Homework 4 Optimization
Spring 2012
Problem 4.1
Problem 26 on page 260 of the textbook.
Solution:
For Steepest Descent we have the result
e(k+1)
A
1 (k)
e
+1
A
1
+1
k+1
e(0)
A.
6 places
Solutions for Homework 3 Optimization
Spring 2012
Problem 3.1
Problem 15 on page 259 of the textbook.
Solution: We have for > 0
xk+1 = xk + k rk , (1 )k k (1 + )k
k =
T
rk rk
T
rk Ark
First note that
Solutions for Homework 2 Optimization
Spring 2012
Problem 2.1
Let A Rnn be a symmetric positive denite matrix, C Rnn be a symmetric nonsingular
matrix, and b Rn be a vector. The matrix M = C 2 is ther
Homework 5 Optimization
Spring 2012
The solutions will be posted on Monday, 3/26/12
Problem 5.1
Problem 1 on page 28 of the textbook.
Solution: Using slack and surplus variables yields the conversion
Homework 1 Optimization
Spring 2012
Problem 1.1
Let f (x) = x3 3x + 1. This polynomial has three distinct roots.
(1.1.a) Consider using the iteration function
1
1 (x) = (x3 + 1)
3
Which, if any, of th
Solutions for Homework 4 Optimization
Spring 2012
Problem 4.1
Problem 26 on page 260 of the textbook.
Solution:
For Steepest Descent we have the result
e(k+1)
A
1 (k)
e
+1
A
1
+1
k +1
e(0)
A.
6 place
Solutions for Homework 3 Optimization
Spring 2012
Problem 3.1
Problem 15 on page 259 of the textbook.
Solution: We have for > 0
xk+1 = xk + k rk , (1 )k k (1 + )k
k =
T
rk rk
T
rk Ark
First note that
Solutions for Homework 2 Optimization
Spring 2012
Problem 2.1
Let A Rnn be a symmetric positive denite matrix, C Rnn be a symmetric nonsingular
matrix, and b Rn be a vector. The matrix M = C 2 is ther
Homework 1 Optimization
Spring 2012
Problem 1.1
Let f (x) = x3 3x + 1. This polynomial has three distinct roots.
(1.1.a) Consider using the iteration function
1
1 (x) = (x3 + 1)
3
Which, if any, of th
Optimization Final Exam
In-class Exam
Open Notes, Textbook, Homework Solutions Only
Calculators Allowed
Due beginning of Class Monday, April 16, 2012
Question
Points
Points
Possible Awarded
1. Basics
Optimization Exam 2
Take-home Exam
Open Notes, Textbook, Homework Solutions Only
Calculators Allowed
Due beginning of Class Monday, April 16, 2012
Question
Points
Points
Possible Awarded
25
25
1. Geom
Optimization Exam 1
Take-home Exam
Open Notes, Textbook, Homework Solutions Only
Calculators Allowed
Due beginning of Class Wednesday, February 29, 2012
Question
Points
Points
Possible Awarded
1. Basi
'
$
Set 20: Constrained Optimization on Rn
Part 8
Kyle A. Gallivan
Department of Mathematics
Florida State University
Optimization
Spring 2012
&
1
%
'
$
Nonlinear Program
min f (x)
subject to:
hi (x)
Optimization Exam 2
Take-home Exam
Open Notes, Textbook, Homework Solutions Only
Calculators Allowed
Due beginning of Class Monday, April 16, 2012
Question
Points
Points
Possible Awarded
25
25
1. Geom
Homework 5 Optimization
Spring 2012
The solutions will be posted on Monday, 3/26/12
Problem 5.1
Problem 1 on page 28 of the textbook.
Solution: Using slack and surplus variables yields the conversion