MAT 168 Optimization (Matthias Köppe; Fall 2020)

MAT 168 Optimization (Matthias Köppe; Fall 2020)

This is a quarter-long upper-division undergraduate course on Mathematical Optimization, held in Fall 2020. Most of 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 …
  • Duality, complementary slackness, dual simplex method
  • Phase 1 + 2 methods
  • Degeneracy + finite termination; the perturbation method
  • Transportation problem + network flow + shortest path problem + max flow problem
  • Integer Programming modeling – fixed cost / network design, Boolean logic, 0-1 Knapsack
  • Branch and bound method for solving general IP
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 2020 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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