Robust Optimization (RO) is a modeling methodology, combined with computational tools, aimed at addressing optimization problems in which the data are uncertain and are only known to belong to some bounded uncertainty set. In the summer school we shall survey the main results of RO as applied to linear, conic quadratic, and semidefinite programming, as well as linear integer programming.

For these cases we show how to derive computationally tractable robust counterparts, exactly or approximately. The relation of RO to chance (probabilistic) constraints will be investigated. We also discuss problems where the uncertainty set is given by historical data ("data driven" optimization) using extensions of RO based on risk measures. For multi-period decision problems we present the Adjustable Robust Optimization (ARO) methodology, which is capable of solving stochastic dynamic problems which are otherwise beyond the reach of traditional methods.

Throughout the lectures we illustrate the power and versatility of RO by presenting applications in diverse fields such as: design of enginnering structures, filter design, signal processing, supply chain management, portfolio optimization and more.

Prerequisites are chapters 1-4 and appendix of these lecture notes.

The school consists of 10 two-hours lectures and 3 afternoon excersise sessions.





July 2

  1. Review of conic optimization
  1. Introduction to RO: Robust linear programs

Exercise Session 1

July 3

  1. Robust linear integer programs
  1. RO and chance constraints

Exercise Session 2

July 4

  1. Data driven RO
  1. Robust conic quadratic optimization

July 5

  1. Robust semidefinite programming
  1. Multi-stage RO

Exercise Session 3

July 6

  1. Robust portfolio optimization
  1. Application of RO in Operations Management

Every day:

10.30-11.00 coffee break
13.00-14.30 lunch
17.00-17.30 coffee break

The social dinner will take place on the night of July 4th and will be charged on site.