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Bartolomeo Stellato

ORF307: Optimization

Previous years: 2022 2023

Main course website: stellato.io/teaching/orf307

Tried to register but the class is full? Fill this Google Form to join the waiting list.

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 branch-and-bound algorithms. A broad spectrum of real-world 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 decision-making 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, 2pm-3:30pm
Website: https://stellato.io
Email: bstellato@princeton.edu

Assistants in instruction

Name: Irina Wang
Office hours: Sherrerd 003, Mondays, 3:30pm-5:00pm
Email: iywang@princeton.edu

Name: Vinit Ranjan
Office hours: Sherrerd 003, Thursdays, 3pm-4:30pm
Email: vranjan@princeton.edu

Name: Pierfrancesco Beneventano
Office hours: Sherrerd 003, Wednesdays, 2pm-3:30pm
Email: pierb@princeton.edu

Name: Jhevon Smith
Office hours: Sherrerd 003, Thursdays, 9:15am-10:45am
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 data-fitting 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
04/16 Midterm 2

Integer Optimization

# Date Topic Slides Homeworks
20 04/18 Integer optimization
21 04/23 Integer optimization algorithms
22 04/25 The role of optimization 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 Python-based 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 (pdf-exported 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 in-class. No coding required.

  • 25% Final Project. 24 hours take-home 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 ODS-approved accommodation, or - as verified by your residential college - a serious illness or an exceptional circumstance.