Course RO: Robust Optimization

Course description:
Optimization problems often contain parameters that are uncertain. The recent methods developed in Robust Optimization try to find solutions that are robust against these uncertainties. The idea is to define a so-called uncertainty region for the uncertain parameters, and then require that the constraints should hold for all parameter values in this uncertainty region. For several optimization problems, and for several choices of the uncertainty region, it has been shown that this so-called robust counterpart problem can be reformulated as tractable optimization problems.

The main topics treated are:

• Uncertain lineair optimization (LO) problems
  • Data uncertainty in LO
  • Tractability of robust counterparts
  • Non-affine perturbations
  • Applications in logistics, marketing, finance, engineering
• Uncertain nonlineair optimization problems
  • Tractability of robust counterparts
  • Examples
• Robust adjustable multistage optimization
  • Adjustable robust counterpart
  • Affine decision rules
  • Non-affine decision rules
• Robust counterpart approximations of scalar chance constraints
  • How to specify an uncertainty set?
  • Chance constraints
  • Safe tractable approximations
• Globalized robust counterparts of uncertain problems
  • Motivation and definition of globalized robust counterpart
  • Computational tractability

Prerequisites:
- Knowledge of basic linear algebra.
-Knowledge of linear programming and duality.
- Basic knowledge of convex analysis and non-linear optimization.

Literature:

- Handouts.
- Lecture notes on Robust Optimization, by Dimitris Bertsimas and Dick den Hertog.

Examination:
Take home problems.

Address of the lecturers:
Prof.dr.ir. D. den Hertog
Faculty of Economics and Business, Section Business Analytics
University of Amsterdam
E-mail: d.denhertog@uva.nl