ISyE4133 Advanced Optimization
Homework 3
Due October 3, 2013
1
Form the Dual and Argue about the Primal
1. Write the complete steps to formulate the dual linear program of the following LP:
min
2x1 + 3x2 + 4x3
s.t. x1 + x2 2
x2 x3 1
x1 0.
2. Is the abov
ISyE4133 Advanced Optimization
Quiz 2
October 9, 2014
Name:
Signature:
GT ID:
We:
0 WORK ALONE. Do not collaborate with anyone.
- Show ALL your work.
a You will only receive credit for the work written on the exam itself or the extra pages I have provided
ISyE4133 Advanced Optimization
Fall 2015
Review Problems Solution
Note: Solutions of Questions 2 to 6 are provided. Question 1 tests on basic concepts and denitions. Fill
them in as an exercise and try to be as precise as possible. Then go through the lec
ISyE 4133 Advanced Optimization
Fall 2015
Syllabus
Instructor
Professor Andy Sun
O ce: Groseclose Room 444
O ce hour: Thursday 1:30-2:30pm
Tel: 404-385-7571 (I prefer that you email me rst.)
Email: andy.sun@isye.gatech.edu
Grader:
Felipe Lagos Gonzalez
Georgia Institute of Technology Atlanta
ISYE 4133 Advanced Optimization
Project 1
Alana Kaplan 902808188
Eduardo Santos 903182854
Young Yoon 902891147
Problem 1.1)
There are two lists and
ISyE4133
Lecture Notes 10: Integer Programming Formulation II
Andy Sun
Nov 5 - 10, 2015
In this lecture, we continue to explore disjunctive constraints and some other useful formulation
techniques using integer programming.
1
Disjunctive constraints
1. Re
ISyE4133
Lecture Notes 11: Integer Hull, Cutting Plane Algorithm, and
Branch-and-Bound Algorithm
Andy Sun
Nov 12 - 17, 2015
In this lecture, we make some important observations about the feasible region of an integer
program, its relation to linear progra
ISyE4133 Advanced Optimization
Homework 1
Due September 3, 2015
1
Portfolio Optimization: An Exercise using XpressMP
The purpose of this question is to give you an introduction to using XpressMP with a simple LP
model. Consider the following problem.
Last
ISyE4133 Advanced Optimization
Homework 2
Due September 17, 2015
1
Is it a polyhedron, a polytope, a convex set?
Recall that a polyhedron is the intersection of a nite number of halfspaces. A polytope is a bounded
polyhedron. A set is a convex set if it c
ISyE4133 Advanced Optimization
Quiz 1
September 18, 2014
Name:
Signature:
GT ID:
Instructions:
0 WORK ALONE. Do not collaborate with anyone.
0 Show ALL your work.
0 You will only receive Credit for the work written on the exam itself or the extra pages I
ISyE4133 Advanced Optimization
Team Project Homework 1
Due October 30, 2014
Instructions
1. Form a group of four people. Email the names of your group members to the grader Yunjie Sun
(yunjie.sun@gatech.edu), and ccd me (andy.sun@isye.gatech.edu) as soon
model DietGen ! Name the model
uses "mmxprs" ! include the Xpress solver package
uses "mmodbc" ! include package to read from Excel
NumFoods := 7146 ! declare how many foods we have
NumNutrients := 30 ! declare how many nutrients we're tracking consumptio
model Kantorovich
uses "mmxprs"; !gain access to the Xpress-Optimizer solver
declarations
W : integer ! the width of the large rolls
m = 4 ! the number of different small rolls demanded
K = 60 ! number of available large rolls
kRange = 1 . K ! t
model CuttingStockColGen ! Name the model
uses "mmxprs" ! include the Xpress solver package
! knapsack function solves the knapsack problem. You will need to write the content of the function in the later part of the code
! here is the initial declaration
model ModelName
uses "mmxprs"; !gain access to the Xpress-Optimizer solver
uses "mmsystem"
n := 3 ! number of variables
m := 1 ! number of coupling constraints
forward function pricing(c: array(range) of real, D : array(range, range) of real, y : array(ra
ISyE4133 Advanced Optimization
Homework 1
Due September 6, 2012
1
LP reformulation
Consider the problem
min
2|x1 + 2| + 3|x2 10|
s.t. x1 + x2 2,
x1 + |2x2 4| 6.
Reformulate it as a linear programming problem.
1.1
Solution
Let us dene w1 = |x1 + 2|, w2 = |
ISyE4133 Advanced Optimization
Homework 2
Due September 19, 2013
1
(25 points) Is it a polyhedron?
For each one of the following sets, determine and explain whether it is a polyhedron, and whether
it is a convex set.
(a) (5 points) A hyperplane.
(b) (5 po
ISyE4133 Advanced Optimization
Quiz 1
September 12, 2013
Name:
Signature:
GT ID:
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work.
You will only receive credit for the work written on the exam itself or the extra pages I hav
ISyE4133 Advanced Optimization
Quiz 2 Solution
October 8, 2013
Name:
Signature:
GT ID:
Instructions:
WORK ALONE. Do not collaborate with anyone.
Show ALL your work.
You will only receive credit for the work written on the exam itself or the extra pages
ISyE4133
Notes 3: The Geometry of Linear Optimization
Andy Sun
September 10, 2015
In this lecture, we discuss the geometry of linear optimization. The goal is to develop a geometric
intuition of the structure of a linear program, as well as an understandi