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
([email protected]
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
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
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 l
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 tr
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: a
from numpy import linalg
import numpy
from numpy import arange
from numpy import *
import numpy as np
from itertools import *
import itertools
A=([1,1,1,0,0,0],[2,1,0
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 usi
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 regi
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
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 s
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 writte
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 th
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)
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
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
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 w
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
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
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