ORF307: Optimization
Main course website: stellato.io/teaching/orf307
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Description
This course focuses on analytical and computational tools for optimization. We will introduce least squares optimization with multiple objectives and constraints. We will also discuss linear optimization modeling, duality, the simplex method, degeneracy, interior point methods and network flow optimization. Finally, we will cover integer programming and branchandbound algorithms. A broad spectrum of realworld applications in engineering, finance and statistics is presented.
Learning objectives
This course introduces analytical and computational tools for mathematical optimization. Upon successful completion of this course you should be able to:

Model decisionmaking problems across different disciplines as least squares, linear and integer optimization problems.

Apply the most appropriate optimization tools when faced with a concrete problem.

Understand which algorithms are slower or faster, and which problems are easier or harder to solve.
Office hours
Instructor
Name: Bartolomeo Stellato
Office hours: Sherrerd 107, Tuesdays, 2pm3:30pm
Website: https://stellato.io
Email: bstellato@princeton.edu
Assistants in instruction
Name: Irina Wang
Office hours: Sherrerd 003, Mondays, 3:30pm5:00pm
Email: iywang@princeton.edu
Name: Vinit Ranjan
Office hours: Sherrerd 003, Thursdays, 3pm4:30pm
Email: vranjan@princeton.edu
Name: Pierfrancesco Beneventano
Office hours: Sherrerd 003, Wednesdays, 2pm3:30pm
Email: pierb@princeton.edu
Name: Jhevon Smith
Oﬀice hours: Sherrerd 003, Thursdays, 9:15am10:45am
Email: jhevon@princeton.edu
Schedule
Lectures
All lectures will take place in Bowen 222 on Tuesdays and Thursdays 11:00am  12:20pm. The schedule is as follows (subject to change):
Least squares
#  Date  Topic  Slides  Homeworks 

1  01/30  Introduction  01_lec.pdf  
2  02/01  Solving linear systems in practice  02_lec.pdf notes  1 Out 
3  02/06  Least squares  03_lec.pdf notes  
4  02/08  Least squares datafitting  04_lec.pdf notes  2 Out 
5  02/13  Multiobjective least squares  05_lec.pdf notes  
6  02/15  Constrained least squares  06_lec.pdf notes  3 Out 
Linear optimization
#  Date  Topic  Slides  Homeworks 

7  02/20  Linear optimization  07_lec.pdf notes  
8  02/22  Piecewise linear optimization  08_lec.pdf notes  4 Out 
9  02/27  Geometry and polyhedra  09_lec.pdf notes  
10  02/29  Applications: data science, control, finance  10_lec.pdf notes  
11  03/05  Simplex method  11_lec.pdf notes  
03/07  Midterm 1  
12  03/19  Simplex method implementation  12_lec.pdf notes  
13  03/21  Duality  13_lec.pdf notes  5 Out 
14  03/26  Duality II  14_lec.pdf notes  
15  03/28  Sensitivity analysis  15_lec.pdf notes  6 Out 
16  04/02  Network optimization  16_lec.pdf notes  
17  04/04  Interior point methods  17_lec.pdf notes  7 Out 
18  04/9  Interior point methods II  18_lec.pdf notes  
19  04/11  Linear optimization review  19_lec.pdf notes  
04/16  Midterm 2 
Integer Optimization
#  Date  Topic  Slides  Homeworks 

20  04/18  Integer optimization  20_lec.pdf notes  
21  04/23  Integer optimization algorithms  21_lec.pdf  
22  04/25  The role of optimization  22_lec.pdf  8 Out 
05/08  Final project out  
05/10  Final project deadline 
Precepts
There will be weekly 50 minutes long precepts. The focus will be on problem solving and Python programming. There are 3 available time slots:
 P01: Tuesdays 7:30pm  8:20pm, Sherrerd Hall 001
 P02: Tuesdays 7:30pm  8:20pm, Andlinger 017
 P03: Wednesdays 7:30pm  8:20pm, Sherrerd Hall 101
Material
The lecture notes are available from the course website and intended to be self contained. The following books are useful as reference texts.
They are either free or digitally available via Princeton University library:
 [LO] D. Bertsimas, J. Tsitsiklis: Introduction to Linear Optimization (available Princeton Controlled Digital Lending)
 [LP] R. J. Vanderbei: Linear Programming: Foundations & Extensions (available on SpringerLink)
 [VMLS] S. Boyd, L. Vandenberghe: Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares (available online)
In this course we strictly follow the crimes against matrices laws!
Precepts material and homework templates are available on the github companion repo.
Prerequisites
 Linear algebra MAT202 and/or MAT204.
 Basic computer programming knowledge suggested.
Software
Students will use the Pythonbased modeling software CVXPY (cvxpy.org) to solve optimization problems arising in several applications in operations research, finance, machine learning and engineering.
The assignments will be using jupyter notebooks running in the jupyterlab environment.
Follow the instructions in this repository to install the complete the environment setup required to run and export all your notebooks. For a quickstart guide on how to use Python, have a look at this guide, especially sections on numpy, scipy, and plotting with matplotlib.
Grading
All submissions should take place on Gradescope (accessible from the Canvas website).

25% Homeworks. 8 weekly homeworks. Almost all of them will include a computational component. Homeworks are due at Friday 9pm EST of following week. Requests for extension on homework will not be accepted, unless there is an extremely valid reason. Homeworks must always be submitted as a single pdf file which includes your written exercises (typed or handwritten) and code (pdfexported jupyter notebook). To export your notebooks to
pdf
from jupyterlab, you should go to: "File" → "Save and Export Notebook As..." → "PDF". 
40% Midterms. Two 80 minutes written exams inclass. No coding required.

25% Final Project. 24 hours takehome final project with written and computational questions.

10% Participation. Students are expected to submit one question or note on each lecture on Ed Forum. The note should summarize what you learned in the last lecture, and highlight the concepts that were most confusing or that you would like to review. A note will receive full credit if: it is submitted before the beginning of next lecture, it is related to the content of the lecture, and it is understandable and coherent. You can make the note private (visible only by you and the course staff) or public, as you choose.
Questions and discussions
Students are encouraged to discuss and ask questions on Ed Forum (accessible from the Canvas website). Please make sure to specify if questions are about General information of the course, about the Lectures or about Homeworks by assigning them to the related category.
Collaboration policy

Homeworks. Students are allowed, and even encouraged, to collaborate on homeworks. When submitting your homework, you are required to list the name of the students you worked with. Also, please write the textbooks, notes or websites that were helpful to you.

Midterms and final project. No collaborations allowed.
Honor code
All work in this course must uphold the University’s commitment to academic integrity. This includes the Honor Code (for written examinations, tests, and quizzes) and guidelines for the submission of original work on all other assignments. More guidance can be found in Rights, Rules, and Responsibilities as well as the handbook Academic Integrity at Princeton.
Attendance
Students are expected to attend each scheduled class on time and ready to participate fully. An excused absence will only be granted in the case of a religious observance, an ODSapproved accommodation, or  as verified by your residential college  a serious illness or an exceptional circumstance.