ECE 580
Spring 2014
FunWork #3
Due on March 12
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you
have taken to solve each problem. Your grade depends on the completeness and
clarity of your work as well as the resulting answer.
Mi
ECE 580
Spring 2014
FunWork #2
Due on February 19
1. Compute the linear, l(x1 , x2 ), and quadratic, q(x1 , x2 ), approximations of the function
f = f (x1 , x2 ) = x3 + x1 x2 x2 x2 ,
1
1 2
at the point x(0) =
1 1
.
2.
(a) Find Df (x) of
2
1 5
f (x) = x
ECE580, Funwork #4
1. (Exercise 12.31) Construct matrices A1 and A2 such that (A1 A2 ) = A A .
2 1
Answer:
1 1
If we set A1 = 0 0 and A2 =
0 0
0.5 0
0.25
and A =
so, A A =
2
2 1
0.5 0
0.25
0.5 0 0
0.5 0 0
1 1
but A =
, then (A1 A2 ) =
1
0.5 0 0
0.5 0 0
0
Fun Work 3
Sumra Bari
March 10, 2015
1
For all the questions I have used Golden Section Search as my line search algorithm.
Following is the MATLAB code for Golden Section Search
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4
5
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7
8
9
10
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12
13
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24
25
function a
ECE 580
Spring 2017
FunWork #1
Due on February 01
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you have
taken to solve each problem. Your grade depends on the completeness and clarity of your
work as well as the resulting answer.
ECE 69500Homework #4
(Due Tuesday, Feb. 21)
This assignment asks you to implement a Mixed Integer Linear Program for the Unit Commitment
problem.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her
ECE 69500Homework #5
(Due Thursday, Mar. 9)
This assignment asks you to solve a few problems on the topic of Power Flow.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work. Handwrit
ECE 69500Homework #2
(Due Thursday, Jan. 26)
This assignment asks you to solve a few problems on Economic Dispatch.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work. Handwritten s
ECE 580
Spring 2017
FunWork #5
Due on April 24
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you have
taken to solve each problem. Use MATLAB to verify your solutions. Include your MATLAB
work. Your grade depends on the completene
ECE 69500Homework #6
(Due Thursday, Mar. 30)
This assignment asks you to solve a few problems on the topic of Security.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work. Handwritt
ECE 69500Homework #3
(Due Thursday, Feb. 9)
This assignment asks you to solve a few problems on Unit Commitment.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work. Handwritten solu
ECE 580
Spring 2017
FunWork #2
Due on February 15
1. Many iterative optimization methods use a variable step size. The step size is determined
by using a line search which involves locating the minimizer of a function of many variables
in a specified dire
ECE 69500Homework #1
(Due Tuesday, Jan. 17)
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work. For this assignment, a typed answer is required. Please email
your answer to me as a
ECE 580 Fun Work #3
Alex Layton
March 9, 2015
Griewank Function
R
From the assignment instructions, a MATLAB
[1] implementation of the Griewank function is the function
griewank.
griewank.m
function [ y ] = g r i e w a n k ( xx )
% Taken from FunWork #3
%
ECE 580
Spring 2017
FunWork #4
Due on March 31
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you
have taken to solve each problem. Your grade depends on the completeness and
clarity of your work as well as the resulting answer.
La
ECE 580 Fun Work #2
Alex Layton
February 19, 2015
1
Problem 1
R
The following MATLAB
[1] output computes the bracket. The answer is interval .
> f = @( x ) 1/2 x 2 sin ( x )
f =
@( x ) 1 / 2 x2 sin ( x )
> x 0 = 0 . 5
x 0 =
0.5000
> e = 0 . 2
e =
0.2000
>
ECE 69500Homework #7
(Due Thursday, Apr. 13)
This assignment asks you to solve a few problems on the topic of Optimal Power Flow.
Instructions: You may discuss homework with your colleagues, but each student is expected to
hand in his/her individual work.
ECE580 Spring 2016
Solution to Problem Set 8
May 1, 2016
1
ECE580 Solution to Problem Set 8:
Linear Programming
These problems are from the textbook by Luenberger and Ye, 3rd edition, which is a
reference for the ECE580 Spring 2016 semester. As such, many
ECE 580
Spring 2009
Funwork #1
Solutions
1.
For the matrix,
1
2
2 1
A=
3 1
1 2
1 3 2
3
2
3
0 1
,
3 3
1 1
nd its rank by rst transforming the matrix by means of the row elementary operations
into an upper triangular form.
Find the rank of the followi
ECE580 Spring 2016
Solution to Problem Set 6
April 10, 2016
1
ECE580 Solution to Problem Set 6
These problems are from the textbook by Chong and Zak, 4th edition, which is the
textbook for the ECE580 Fall 2015 semester. As such, many of the problem statem
ECE580 Spring 2016
Solution to Problem Set 4
February 17, 2016
1
ECE580 Solution to Problem Set 4:
Newtons and Gradient Algorithms
These problems are from the textbook by Chong and Zak, 4th edition, which is the
textbook for the ECE580 Spring 2016 semeste
ECE580 Spring 2016
Solution to Problem Set 2
February 1, 2016
1
ECE580 Solution to Problem Set 2
These problems are from the textbook by Chong and Zak, 4th edition, which is the
textbook for the ECE580 Spring 2016 semester. As such, many of the problem st
ECE580 Spring 2016
Solution to Problem Set 5
April 10, 2016
1
ECE580 Solution to Problem Set 5
These problems are from the textbook by Chong and Zak, 4th edition, which is the
textbook for the ECE580 Fall 2015 semester. As such, many of the problem statem
ECE580 Spring 2016
Solution to Problem Set 1
October 4, 2016
1
ECE580 Solution to Problem Set 1
These problems are from the textbook by Chong and Zak, 4th edition, which is the
textbook for the ECE580 Spring 2016 semester. As such, many of the problem sta
19. Problems with Equality Constraints a
19.1 W
a. As usual, let f be the objective function, and h the constraint function. We form the Lagrangian l(a:, A) =
f (m) + ATh(a:), and then ﬁnd critical points by solving the following equations (Lagrange condi
ECE 580
Spring 2008
Funwork #5
Due on April 16
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you have
taken to solve each problem. Your grade depends on the completeness and clarity of your
work as well as the resulting answer. O-
ECE 580
Spring 2014
FunWork #4
Due on March 28
INSTRUCTIONS: The assignment must be typed. Clearly identify the steps you have
taken to solve each problem. Your grade depends on the completeness and clarity of your
work as well as the resulting answer.
1.
ECE 580
Spring 2009
Funwork #3
Solutions
1. The Taylor series expansion of a function f(x) about x=x0 is
f ( k ) ( x0 )
f ( x0 )
f ( x0 )
f ( x) =
( x x0 ) k = f ( x 0 ) + f ( x0 )( x x0 ) +
( x x0 ) 2 +
( x x 0 ) 3 + .
k!
2!
3!
k =0
Since f ( x) = cos x