MAT 168 Optimization (Matthias Köppe; Winter 2023)

MAT 168 Optimization (Matthias Köppe; Winter 2023)
This is a quarter-long upper-division undergraduate course on Mathematical Optimization, held in Winter 2023. The videos are lightly edited versions of synchronously held lectures. All notes were written in real time.

The following topics are covered in this course:

  • Modeling: Examples of optimization problems.
  • Graphical method for solving linear programs with 2 variables
  • AMPL: a software for modeling and solving linear programs
  • Simplex method: dictionary of simplex method, pivoting, ratio test …
  • Convex geometry
  • Duality, complementary slackness, dual simplex method
  • Phase 1 + 2 methods
  • Degeneracy + finite termination; the perturbation method
  • Assignment problems, network flows
  • Integer Programming modeling – fixed costs, Boolean logic, piecewise linear functions, stable set
The approach to developing LP theory and the notation for the simplex method follow the textbook by Robert J. Vanderbei, Linear programming, foundations and extensions.

Videos and all other materials are copyright 2023 Matthias Köppe and shared as Open Educational Resources subject to the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license.

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 Matthias Koeppe
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