Optimization under Uncertainty: an introduction with practice

Slides and material for my short introductory course (9 hours) on Optimization under Uncertainty, given at CentraleSupélec, campus of Rennes is available on HAL/CEL:

https://cel.hal.science/hal-05547452v1

It has two chapters:

  1. Static & two-stage problems
  2. Multitemporal & dynamic programming

Course archive content

The HAL/CEL website puts to the front only the slides, while the rest of the material is provided in a zip archive with:

    • Exercises: "abc cost", news vendor, inventory control
    • Extra material: CVaR cast as a linear program
    • Solution to computer based exercises in the `Matlab live code` directory (one per year, with some variations between them).

    Some illustrations from the slides

    The subjective matter of risk aversion which emerges when cost becomes uncertain: which decision (a or b) is preferable?

    Plot of the pdf of two random cost alternatives (a vs b), in which none is clearly preferable. Any of the two can be selected depending on which part of the distribution is focused.

    CVaR definition, illustrated on a PDF plot:

    CVaR definition, illustrated on a PDF plot

    Two-stage stochastic programming, depicted as tree graph:

    Two-stage stochastic programming, depicted as tree graph

    Dynamic Programming algorithm illustrated (an attempt):

    Dynamic Programming algorithm illustrated

    Remark: those illustrations are created with Inkscape. While the course archive doesn't contain the SVG sources for keeping it tidy, please contact me if you'd like the editable version.