IE5531 Assignment 1
Due in class (12pm), Sept 16th
Problem 1 (20pts). A company produces two kinds of products. A product of the rst type
requires 1/4 hours of assembly labor, 1/8 hours of testing, an
IE 5531 2013 Fall
Assignment 7 Solution
Problem 1
1. False. Consider the following counterexample:
f (x) = x
convex
g(x) = x2
convex
f (g(x) = x2 concave
2. True.
Proof Let h(x) = f (g(x),
h (x) = f (
IE5531 Assignment 9
Due in class (12pm), Nov 27th
Problem 1. (30pts) Use branch-and-bound method to solve the following integer program.
You are allowed to use LP solver to solve each linear program.
IE 5531 2013 Fall
Assignment 1 Solution
1.(a) Let x1 be the number of type 1 product, and x2 be the number of type 2 product.
maximize (9 1.2)x1 + (8 0.9)x2
1
s.t.
x + 1 x2 90
4 1
3
1
x1 + 1 x2 80
8
3
IE 5531 Sample Final Exam - Dec 2013
Page 1 of 8
S AMPLE F INAL E XAM S OLUTION
IE 5531
Dec, 2013
INSTRUCTIONS
a) Write ALL your answers in this exam paper.
b) Two pieces of notes are allowed. No comp
IE5531 Assignment 8
Due in class (12pm), Nov 20th
Please attach the code for all your problems (and the gures as required)
Problem 1 (25pts). Write a computer code in MATLAB using bisection method to
IE 5531 Practice Final Exam
Prof. John Gunnar Carlsson
December 7, 2010
1
Integer programming
1. Use implicit enumeration to solve the integer program
minimize 7x1 + 3x2 + 2x3 + x4 + 2x5
4x1 + 2x2 x3
IE5531 Assignment 5/Sample Midterm Exam
Due in class (12pm), Oct 23rd
Note: This homework is also the sample midterm. The solution is on Moodle.
However, please do it without looking at the solution r
Lecture 16: More on KKT Conditions and Convexity
Zizhuo Wang
University of Minnesota
Nov, 2013
Zizhuo Wang (University of Minnesota)
Engineering Optimization: Lecture 16
Nov, 2013
1 / 29
Announcement
IE5531 Assignment 3
Due in class (12pm), Oct 2nd
Problem 1 (20pts). Consider the following linear program:
maximize 500x1 + 250x2 + 600x3
subject to 2x1 + x2 + x3 240
3x1 + x2 + 2x3 150
x1 + 2x2 + 4x3
IE5531 Assignment 4
Due in class (12pm), Oct 14th, Monday
Problem 1 (20pts). Consider the following linear program:
maximize
5x1 + 2x2 + 5x3
subject to 2x1 + 3x2 + x3 4
x1 + 2x2 + 3x3 7
x 1 , x2 , x3
IE 5531 2013 Fall
Assignment 2 Solution
Problem 1
1. True. Set P lies in an ane subspace dened by m = n 1 linearly independent constraints of dimension one. Every solution of Ax = b is of the form x0
Lecture 24: Final Review
Zizhuo Wang
University of Minnesota
Dec, 2013
Zizhuo Wang (University of Minnesota)
Engineering Optimization: Lecture 24
Dec, 2013
1 / 44
Final Exam
Final exam next Wednesday,
IE 5531 2013 Fall
Assignment 6 Solution
Problem 1
1. By rst order necessary condition
f (x ) = 0, we have
4x + y 6 = 0
x + 2y 7 + z = 0
2z 8 + y = 0
6
Solving the above equations, we get a minimum can
IE 5531 Final Exam - Dec 2013
Page 1 of 9
F INAL E XAM S OLUTION
IE 5531
Dec 11th, 2013
INSTRUCTIONS
a) Write ALL your answers in this exam paper.
b) Two pieces of notes are allowed. No computer or ce
IE 5531 Midterm - Oct 2013
Page 1 of 9
M IDTERM E XAM
IE 5531
Oct 21st, 2013
INSTRUCTIONS
a) Write ALL your answers in this exam paper.
b) One piece of note is allowed. No computer or cell phone is al
IE5531 Assignment 1
Due in class (12pm), Sept 21st
For those questions that ask you to write MATLAB codes to solve the problem. Please
print the code and attach it to the homework. You also need to wr
IE5531 Assignment 6
Due in class (12pm), Nov 4th
Problem 1 (20pts). Consider the function
f (x, y, z) = 2x2 + xy + y 2 + yz + z 2 6x 7y 8z 9
1. Use the rst-order necessary conditions, nd the candidate
IE 5531 Sample Final Exam - Dec 2013
Page 1 of 9
S AMPLE F INAL E XAM
IE 5531
Dec, 2013
INSTRUCTIONS
a) Write ALL your answers in this exam paper.
b) Two pieces of notes are allowed. No computer or ce
IE5531 Assignment 7
Due in class (12pm), Nov 13th
Problem 1 (25pts). Either prove or nd a counterexample for each of the following
statement (you can assume all the functions are second order continuo
IE5531 Assignment 1
Due in class (12pm), Sept 25th
Problem 1 (25pts). Consider an LP in its standard form and the corresponding constraint
set P = cfw_x|Ax = b, x 0. Suppose that the matrix A has dime
IE 5531 Fall 2013
Assignment 8 Solution
Problem 1
Before we use bisection method to solve the problem, we can check the number of solutions and
the intervals from looking at the graph. The graph shows
IE 5531: Engineering Optimization I
Lecture 3: Linear Programming, Continued
Prof. John Gunnar Carlsson
September 15, 2010
Prof. John Gunnar Carlsson
IE 5531: Engineering Optimization I
September 15,
IE 5531: Engineering Optimization I
Lecture 3: Linear Programming, Continued
Prof. John Gunnar Carlsson
September 15, 2010
Prof. John Gunnar Carlsson
IE 5531: Engineering Optimization I
September 15,
IE 5531: Engineering Optimization I
Lecture 2: Linear Programming
Prof. John Gunnar Carlsson
September 13, 2010
Prof. John Gunnar Carlsson
IE 5531: Engineering Optimization I
September 13, 2010
1 / 30
IE 5531: Engineering Optimization I
Lecture 5: The Simplex method, continued
Prof. John Gunnar Carlsson
September 22, 2010
Prof. John Gunnar Carlsson
IE 5531: Engineering Optimization I
September 22,
IE 5531 2013 Fall
Assignment 4 Solution
Problem 1
1. Dual problem:
minimize 4y1 + 7y2
s.t.
2y1 + y2 5
3y1 + 2y2 2
y1 + 3y2 5
y 1 , y2 0
2. From the graph, we can get the optimal solution for the dual
Lecture 3: The Geometry of Linear Optimization
Zizhuo Wang
Department of Industrial and Systems Engineering
University of Minnesota
Sep 16th, 2015
Zizhuo Wang
Engineering Optimization: Lecture 3
Annou
IE 5531: Engineering Optimization I
Lecture 6: Simplex method topics, duality
Prof. John Gunnar Carlsson
September 27, 2010
Prof. John Gunnar Carlsson
IE 5531: Engineering Optimization I
September 27,
IE 5531 Midterm - Oct 2017
Page 1 of 9
M IDTERM E XAM S OLUTION
IE 5531
Oct 25th, 2017
INSTRUCTIONS
a) Write ALL your answers in this exam paper.
b) One piece of note is allowed. No computer or calcul
Lecture 15: Optimality Conditions
Zizhuo Wang
Department of Industrial and Systems Engineering
University of Minnesota
Oct 31st, 2016
Zizhuo Wang
Engineering Optimization: Lecture 15
Announcements
I
H
Lecture 24: Final Review
Zizhuo Wang
Department of Industrial and Systems Engineering
University of Minnesota
Dec 7th, 2016
Zizhuo Wang
Engineering Optimization: Lecture 24
Final Exam Logistics
Time:
Lecture 22: Integer Optimization Algorithms
Zizhuo Wang
Department of Industrial and Systems Engineering
University of Minnesota
Nov 30th, 2016
Zizhuo Wang
Engineering Optimization: Lecture 22
Announc
Lecture 12: Interior Point Method
Zizhuo Wang
Department of Industrial and Systems Engineering
University of Minnesota
Oct 17th, 2016
Zizhuo Wang
Engineering Optimization: Lecture 12
Midterm Exam
Midt