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Optimization Methods

Graduate · Historical course

Fall 2009

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods.

Readings

  • Assigned chapters are from the required textbook: Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization . Belmont, MA: Athena Scientific, 1997. ISBN: 9781886529199.
    Listed reading
  • LEC #: 1 · TOPICS: Applications of linear optimization · READINGS: Chapter 1
    Reading assignment
  • LEC #: 2 · TOPICS: Geometry of linear optimization · READINGS: Chapter 2
    Reading assignment
  • LEC #: 3-4 · TOPICS: Simplex method · READINGS: Chapter 3
    Reading assignment
  • LEC #: 5-6 · TOPICS: Duality theory · READINGS: Chapter 4
    Reading assignment
  • LEC #: 7 · TOPICS: Sensitivity analysis · READINGS: Chapter 5
    Reading assignment
  • LEC #: 9 · TOPICS: Large scale optimization · READINGS: Chapter 6
    Reading assignment
  • LEC #: 10-11 · TOPICS: Network flows · READINGS: Chapter 7
    Reading assignment
  • LEC #: 12 · TOPICS: Applications of discrete optimization · READINGS: Chapter 10
    Reading assignment
  • LEC #: 22 · TOPICS: Interior point methods · READINGS: Chapter 9
    Reading assignment
  • LEC #: 23-24 · TOPICS: Semidefinite optimization · READINGS: Freund, Robert. “Introduction to Semidefinite Programming.” ( PDF ) (Used with permission.) ↗
    Reading assignment
Sources