Math 171A Homework Assignment # 2
Due Date: January 23, 2014
1. (10 points) Consider the linear system Ax = b where
3
3
6
4
2 3
3
6
6
0 ,
A= 1
b= 1
2
1
0
1
6
3
0
5
.
Determine the rank of A and
Section 1.3
4.
6.
.
10.
[
]
[
]
[
]
[ ].
12. Yes, b is a linear combination of a1, a2, and a3.
14. Yes, b is a linear combination of the columns of A.
16. h = 2.
18. Non-integer weights are acceptable
Math 171A Homework Assignment # 3
Due Date: January 31, 2014
1. (10 points) Let F = cfw_x R2 : 1 x1 x2 1, x2 0. Describe
the sets of vectors c such that:
(a) cT x is bounded from below but unbounded f
Section 1.1
4. The line equations are:
.
The augmented matrix is:
[
].
To eliminate x1 term in second equation, add (-3) times row 1 to row 2.
[
]
Multiply row 2 by -1/8 in order to obtain 1.
[
]
The
Math 171B: Numerical Optimization: Nonlinear Problems
Instructor: Michael Holst
Spring Quarter 2015
Solutions for Homework Assignment #1
Exercise 1.1. If x is an eigenvector of A, show that x is also
Math 171B: Numerical Optimization: Nonlinear Problems
Instructor: Michael Holst
Spring Quarter 2015
Solutions for Homework Assignment #2
Exercise 2.1. Sketch F (x) = 1/x a for a = 2. Then derive a New
Math 171B: Numerical Optimization: Nonlinear Problems
Instructor: Michael Holst
Spring Quarter 2015
Solutions for Homework Assignment #3
Exercise 3.1. Let H be a symmetric matrix with spectral decompo
Math 171B: Numerical Optimization: Nonlinear Problems
Instructor: Michael Holst
Spring Quarter 2015
Solutions for Homework Assignment #4
Exercise 4.1. Let f (x) denote a convex continuously differenti
Math 171B: Numerical Optimization: Nonlinear Problems
Instructor: Michael Holst
Spring Quarter 2015
Solutions for Homework Assignment #5
Exercise 5.1. Consider the nonlinearly constrained problem
mini
Tentative Schedule of Math 171A, Winter 2014
Jiawang Nie
The textbook is Linear Programming (by Philip Gill et al., 1998). To obtain an electronic copy,
send a request email to the instructor.
Week 1:
Math 171A Practice Midterm II
Notes: 1) For computational problems, no credit will be given for unsupported answers
gotten directly from a calculator. 2) For proof problems, no credit will be given fo
What is optimization?
Lecture 1
Introduction to Optimization
Websters dictionary:
UCSD Math 171A: Numerical Optimization
Optimization the process or method for making something
(design, system, decisi
Math 171A Homework Assignment # 4
Due Date: February 14, 2014
1. (10 points) Consider the feasible set F dened by the following constraints
x1 + x2 4,
x1 + 3x2 6,
6x1 x2 18,
3 x2 6,
x1 1.
(a) Express
Math 171A Homework Assignment # 1
Due Date: Thursday, January 16, 2014
1. (10 points) Find the minimizer of the following LP:
cfw_
minimize 7x1 9x2
subject to 3x1 + 4x2 5, 5x1 + 3x2 4, 4x1 5x2 3, 4x1
Section 1.9
4. [
]
8. [
]
10. [
]
12. The transformation T in Exercise 10 maps e1 into e2 and maps e2 into e1. A
counterclockwise rotation about the origin through /2 radians also maps e1 into e2 and
Section 2.1
[
2.
], 2C 3E is not defined,
[
], EC is not defined.
[
4.
(
)
],
[
].
[
6. a.
],
[
],
( )
( )]
( )
[
b.
[
].
[
].
8. B has 5 rows.
[
10.
].
12. By inspection of A, a suitable column for B
Section 1.7
[ ]
2. Let
[ ]
[
[
]
]
[
[
]
]. Consider the equation:
.
The augmented matrix is:
[
].
Interchange row 1 and row 3, and add 2 times row 1 to (-3) times row 2:
[
].
It is clear that there a