University of Cambridge > Mathematics > Statistical Laboratory > Richard Weber > Optimization

 This material is provided for students, supervisors (and others) to freely use in connection with this course. Copyright remains with the author.

Optimization IB

picture of feasible set for P Constraints for problem P

This is home page for a course of 12 lectures to first and second year Cambridge mathematics students.

There is a more modern version of this course here.

Each lecture is as self-contained as possible and has course notes amounting to four or five A4 pages. Click here for the table of contents.

I have also made additional notes about things I said in lectures and questions students have asked.

There is a single examples sheet and a file of exam questions. Students should receive two supervisions on the examples sheet. There are two recommended books. If you enjoy this course then you should consider related courses in Part II and other items of interest.

Course notes

How to view and print: There are 56 pages of notes available as a pdf file. The notes are formatted as two side-by-side pages per A4 sheet.

Where to collect photocopies of the notes: You can find copies of notes by using this map to locate the Statistical Laboratory pigeonholes.

Examples sheets

There is a single examples sheet, available as a pdf file of 6 pages. The topics that the questions cover appear in the same order as topics are covered in lectures and you will find a recommendation on the sheet concerning the work you should do for your supervisions. Viewing and printing is identical as for the notes above.


I include a small (non-examinable) digression half way through each lecture.

Topics I have covered are:

  1. set partitioning
  2. job scheduling
  3. optimal electricity generation and distribution
  4. insects as optimizers
  5. project assignment in CUED
  6. examples of very large LPs
  7. how large an LP can we solve?
  8. on-line bin packing
  9. airline luggage
  10. MacDiet problem
  11. hanging chain
  12. hanging springs puzzle
  13. string covering (an open problem)
  14. Braess's paradox
  15. more examples of very large LPs
  16. rendezvous problem
These examples and other material are included in this file of overhead projector slides. Additional notes
Here are some additional notes which summarise things I said in lectures and which do not appear in the printed notes. I have also made notes about questions that students asked, either in lectures or by coming up to me afterwards.

Exam questions

Here is single fille of all Tripos questions on Optimization for the years 2004-2011

This file has exam questions from 1985-1997.

Recommended books

  1. Bazaraa, M., Jarvis, J. and Sherali, H., Linear Programming and Network Flows. second edition, 1990, Wiley.
  2. Luenberger, D., Introduction to Linear and Non-Linear Programmings, second edition, 1984, Addison-Wesley.

Related courses

There are two courses in Part II that build on what students learn in this course. In Part IIA there is Algorithms and Networks. In Part IIB there is Optimization and Control.

Other items of interest

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Last modified: 17 Janaury 2007