Advanced Topics in Optimization

Nonlinear, Convex Optimization

Book and Slides from Convex Optimization – Boyd and Vandenberghe

Andrzej Ruszczynski. 2006. Non Linear Optimization.

Mokhtar S. Bazaraa, Hanif D. Sherali, C.M. Shetty. 2006. NonLinear Programming

Focus:

  • Applications
  • Algorithmic
    • KKT conditions + Interior Point Methods (Chp 11 of Boyd’s book - the slides are online or Bazaraa’s book or Vanderbei’s book ‘Linear Programming’ ch 17-21).

Exercises:

  • Exercises from Boyd’s page linked above
  • Applications: Part II (chp 6,7,8) of Boyd’s book using https://www.cvxpy.org/
  • Implementation of interior point in python

Bilevel Programming

Martin Schmidt. A Gentle and Incomplete Introduction to Bilevel Optimization. Slides Article

Martin Schmidt. BOBILib: Bilevel Optimization (Benchmark) Instance Library Talk at the ISMP 2024 (Slides) July 24, 2024. Montréal, Canada

Exercises by Martin Schmidt (available on request)

Mixed Integer Non Linear Optimization

Pietro Belotti, Christian Kirches, Sven Leyffer, Jeff Linderoth, James Luedtke and Ashutosh Mahajan (2013). Mixed-integer nonlinear optimization. Acta Numerica, 22, pp 1­131 doi:10.1017/ S0962492913000032

Martin Schmidt (2021). Mixed-Integer Nonlinear Optimization Slides

Exercises from Martin Schmidt (available on request)