Order of introduction to shadow prices, duality, and KKT

[brynpickering]

Currently (v2024-10-07), the order of more meaty content is:

1. introduction to shadow prices via (marginal) sensitivity analysis
2. introduction to the dual problem as a method to calculate shadow prices
3. introduction to KKT to better describe the link between the primal and dual problems
4. introduction to power market optimisation and the link between the market-clearing price and the shadow price

This feels a bit like jumping in the deep end before students can swim. It also necessitates separating other forms of - and methods to handle - uncertainty so that the main point concerning shadow prices can be introduced and expanded upon.

A more natural flow might be to introduce MILP and power markets following the LP intro. This keeps things graphical while adding incrementally to the complexity of the optimisation problem. Then shadow prices can be introduced, by posing the question "how do we ascertain the market clearing price from the optimisation problem describing the power market?". In that context, I would perhaps (a) bring in uncertainty as a separate topic later on, but cover it more thoroughly and (b) introduce KKT as more of an aside for the keener students. Then again, it may be that students being able to explain or derive the dual problem via KKT conditions are some of the key course learning objectives!