Course Syllabus

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This is a graduate course on Numerical Optimization with minimal prerequisites.

  • Linear algebra (vectors, matrices, tensors, spectral theory, decompositions, factorizations)
  • Multivariable calculus (gradients, Jacobians, Hessians, Levi-Civita connection;)
  • Principles of numerical computation (floating point arithmetic, error analysis, condition)
  • Command of Python or another programming language that gives access to mathematical optimization packages

The lectures take place on Zoom, and minimally edited recordings are posted to https://video.ucdavis.edu/channel/channelid/297451122

Office hours

All office hours take place on Discord, see Announcements for the invite link. I have set aside Tuesdays and Thursdays 7:30pm–8:30pm as office hours for this class. You are very welcome to join for talking with me about anything related or unrelated to the class. I'm also happy to make individual or group appointments and to interact on Discord throughout the week.

Grading

The course grade is based on 80% Homework projects and 20% Peer grading duties.

Some literature and resources

Textbooks

Robert Vanderbei, Linear Programming: Foundations and Extensions. Available as an e-book, for free, through the UC Davis Library and SpringerLink. This is the book that I use in my undergraduate class on Optimization (videos from Winter 2023;  videos from Fall 2020).

Jorge Nocedal and Stephen J. Wright, "Numerical Optimization", 2nd edition, ISBN 0-387-30303-0. Available as an e-book, for free, through the UC Davis Library and SpringerLink.

S. Boyd and L. Vandenberghe, Convex Optimization. Available as an e-book, for free, from this link.

Aharon Ben Tal and Arkadi Nemirovski's lecture notes, in particular Lectures on modern convex optimization (2023) – analysis, algorithms, engineering applications

Software (Python)

CVXpy

SageMath 10.0.beta7

Geomstats

Research articles

Parallelizing the dual revised simplex method, Q. Huangfu and J. A. J. Hall, Mathematical Programming Computation, 10 (1), 119-142, 2018. DOI: 10.1007/s12532-017-0130-5

Course Summary:

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