Part I: Linear programming

	Lecture topic	Video	Dates	Julia notebooks used in class
1.	Introduction Part I			Top Brass
2.	Introduction Part II			Top Brass 2, Top Brass 3
	Julia tutorial			Julia commands
3.	Linear programs	video		Standard Form
4.	Minimax and planning	video		Chebyshev, House
5.	Network flow problems	video		Sailco, Millco, Swim Relay
6.	LP duality	video		Top Brass dual
7.	Dual flows and algorithms	video		none

Part II: Convex programming

	Lecture topic	Video	Dates	Julia notebooks used in class
8.	Least squares	video		Regression
9.	Equality constraints and tradeoffs	video		Moving Average, uy_data, Hovercraft
10.	Regularization	video		Data Norm, Hover 1D
11.	Quadratic forms and ellipsoids	video		none
12.	QPs and QCQPs	video		Portfolio, folio_mean, folio_cov
13.	Cones and semidefinite constraints	video		none
14.	Convex programming	video		none
15.	Duality	video		none
16.	Review of convex optimization	video		none
	Class project and Q&A	video		Structural optimization

Part III: Nonconvex and combinatorial models

	Lecture topic	Video	Dates	Julia notebooks used in class
17.	Introduction to nonconvex models	video		Knapsack
18.	Rounding and relaxation	video		none
19.	Fixed costs and variable bounds	video		ClothCo, UFL
20.	Logic constraints and integer variables	video		Sudoku
21.	Set cover and TSP	video		CuttingPipe, TSP
22.	Quadratic assignment and SOS	video		QAP, SOS
23.	Cutting planes and branch & bound	video		none
24.	Nonlinear programming	video		Tires, Polygon, Navigation
25.	NLP algorithms	video		Iterative Methods

Textbook:

There is no required textbook for the class. All course material will be presented in class and/or provided online as notes. That being said, there are several textbooks that cover parts of what we will see in class, and you may find it helpful to use them as references. Here are a few:

• S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
  The book is available for free here: http://stanford.edu/~boyd/cvxbook/.
• H.P. Williams. Model Building in Mathematical Programming, 5th Edition. Wiley, 2013.
• R.L. Rardin. Optimization in Operations Research. Prentice Hall, 1998.

Coding:

You will be required to write code in Julia (http://julialang.org/), a programming language similar to Matlab and Python. We will also use the JuMP modeling language, which is a Julia module (Official JuMP documentation).

• Download JuliaPro. It comes bundled with the IJulia notebook and several popular packages, including JuMP.
• Alternatively, you may run Julia in your browser using JuliaBox. Simply log in with any Google account and create a new file using “Julia 0.6.2”. This method will get you started instantly but is perhaps less reliable in the long run.

Here are some additional useful references:

• Noteworthy differences from other languages.
• Another cheatsheet comparing Julia syntax to other languages.
• Learn X in Y minutes Julia tutorial.
• Official Julia documentation.
• A handy cheat-sheet.

You will also be using the IJulia notebook:

• IJulia documentation
• Markdown cheatsheet
• Equations formatted using $…$ in LaTeX.
• Another reference sheet for LaTeX can be found here.

We also had an hour-long Julia + IJulia + JuMP tutorial in class.

• Here are the slides.

Official syllabus:

The official syllabus for the class is available here.

Important dates:

• Tue Jan 23: first lecture
• Thu Mar 22: midterm exam (7:15–9:15pm, Ingraham Hall B10)
• Tue Mar 27 and Thu Mar 29: spring break (no classes)
• Fri Apr 6: project proposal is due
• Thu May 3: last lecture
• Mon May 7: final project report is due
• Other important dates: https://registrar.wisc.edu/spring_deadlines_at_a_glance.htm

Grading:

There will be three main components to your grade:

• Homework: 45%. There are weekly (roughly) homework assignments (8-10 total). These will be graded on a coarse 4-point scale. You get 4 points if you attempted all problems and got everything mostly right.
• Midterm exam: 25%. There will be an exam before spring break where you will be tested on all the material covered up to that point. The exam will be taken outside of regular class hours (see date and time above) so be sure that you have no scheduling conflicts. It is your responsibility to ensure that you are available and present for the midterm exam.
• Project: 30%. There will be a group project due at the end of the semester. More information here.

There is no final exam for this class.

Letter grades will be assigned according to the following hard cut-offs: A: 93% or higher, AB: 87%, B: 80%, BC: 70%, C: 60%, D: 50%, F: less than 50%. I reserve the right to lower any of these cut-offs at my discretion. In other words, any changes I make can only cause your letter grade to stay the same or improve.

More information about homework assignments

• Homework assignments are due Sunday by 11pm. They can be turned in up to two days late at a penalty of -25% per day. Solutions will be posted to the class website on Wednesday.
• Exceptions will be made to the rules above in order to accommodate special circumstances. This includes family or medical emergencies, religious observances, and documented disabilities. If you have a special circumstance and foresee a conflict, please email the instructor as soon as possible to make alternative arrangements.
• Assignments must be turned in electronically (as PDF or images) via gradescope. For a tutorial on how to do this, please watch this video. If you’ll be scanning documents in using a camera phone, read this guide.
• Problems requiring code must be solved using an IJulia notebook. You must turn in a PDF version of your notebook. Do not turn in raw code such as an .ipynb or .jl file. The easiest way to turn a notebook into PDF is to use your browser’s “print to PDF” function. Be sure to compile your file (so we can see the outputs) before you turn it in.
• For problems not requiring code, you may write up solutions by hand or electronically (e.g. using Word, LaTeX, or an IJulia notebook). Either way, you must turn it in electronically.
• Start each problem on a new page if possible. At the very least, be sure that each new problem is clearly indicated (use a large heading in Markdown to indicate each new problem, for example). If a problem has multiple parts, it’s OK to answer them on a single page.
• Start early. You have two weeks (three weekends) to complete assignments, so you can expect them to take longer than standard one-week problem sets. They are also worth a significant portion of your final grade. You have plenty of opportunities to get help during office hours or via Piazza, so the earlier you get started, the better!
• Explain your work. This means write in words how you solved the problem, use intuitive variable names, and comment any code you turn in. It is unacceptable to simply turn in undocumented code. Even if your code produces the correct result, you will likely lose points.
• You are encouraged to discuss homework problems with classmates and even work in groups. However, the work you turn in must be your own. If you use any external sources (e.g. the internet) be sure to cite your sources!

The goal of the class project is to explain, model, and solve an optimization problem using techniques we learned in class. It’s an opportunity to pursue that idea you’ve been thinking about for some time but didn’t know how to best approach it! Some students also bring in problems related their own graduate or undergraduate research.

Here are some of the top projects from the Spring 2018 semester (alphabetical by first author) — check them out!

Authors	Project title	Files
Om Bathija	Pay Me Maybe: Settle Group Bills	Notebook, Data
Katie Biegel and Alex Tanke	Going for Baroque: Scheduling an Artistically Meritorious and Financially Feasible Symphony Orchestra Season	Notebook, Data
Alex Dawson-Elli, Patrick Dills, and Kieran Nichols	Trajectory Optimization using Direct Collocation	Notebook, Data
Jacob Johnson	Strategic Amortization of Multiple Student Loans	Notebook, Data
John Sandgren, Benjamin Morris,   Abigail Purfuerst, and Casey Kong	National Park Optimization	Notebook, Data
Jay Wang	CS 506 Group Assignment Optimization	Notebook, Data

Here are some of the top projects from the Spring 2017 semester:

Authors	Project title	Files
Ian Atkins	Indoor Farm HVAC Optimization	Notebook, Data
Tuan Dinh and Varun Sah	Determining Winning Strategies Using Game Theoretic Optimization	Notebook, Data
Bailey Flanigan and Andrew Duplissis	Optimizing the WIMR Elevators	Notebook, Data
Yash Govind and Hakan Memisoglu	Optimizing Scheduling for Dataflow program	Notebook, Data
Alex Haufler and Patrick Forbes	Optimally Uniform Magnetic Fields Using Discrete Circular Electromagnetic Coils	Notebook, Data
Yiqiu Zhang and Jia Zhuang	Forest Harvest Company Distribution Optimization	Notebook, Data

Here are some of the top projects from the Spring 2016 semester:

Authors	Project title	Files
Aritra Biswas and Prathusha K. Sarma	Wanderlust: Optimizing Group Travel Plans	Notebook, Data
Wayne Chew and Sahit Mandala	Fiber Optic Network Topology Optimization	Notebook, Data
Christopher E. Lawson, Lise O. Aagesen, and Eric C. McCurry	Dynamic Metabolic Modelling of Nitrifying Consortia	Notebook, Data
AJ Nosek and Newton Wolfe	Minimizing Economic and Public Health Impacts of Radioactive Contamination	Notebook, Data
Nate Pritzl and Logan Colla	Fantasy Football Roster Optimization	Notebook, Data
Peter Schlafly and Sam Olson	Selecting the Best Possible NHL Expansion Team	Notebook, Data
Michael Scott and Drew Patenaude	Optimization of Trajectories through Dynamical Gravitational Systems	Notebook, Data
Ananth Sridhar, Rangapriya Parthasarathy, and Song Mei	Image Mosaicking	Notebook, Data
Jennifer Witt	Optimizing Telescope Time	Notebook, Data
Haojun Zhang and Keyi Cui	Using Optimization for Task Scheduling	Notebook, Data