Integrality

There's nothing special about binary and integer variables in SDDP.jl. Use them at will!

If you want finer control, you can pass an SDDP.AbstractDualityHandler to the duality_handler argument of SDDP.train.

See the Duality handlers section for the list of options you can pass.

Breaking changes in SDDP.jl v0.4

SDDP.jl v0.4.0 introduced a number of breaking changes in how we deal with binary and integer variables.

Breaking changes

• We have renamed SDDiP to SDDP.LagrangianDuality.
• We have renamed ContinuousRelaxation to SDDP.ContinuousConicDuality.
• Instead of passing the argument to SDDP.PolicyGraph, you now pass it to SDDP.train, e.g., SDDP.train(model; duality_handler = SDDP.LagrangianDuality())
• We no longer turn continuous and integer states into a binary expansion. If you want to binarize your states, do it manually.

Why did we do this?

SDDiP (the algorithm presented in the paper) is really two parts:

1. If you have an integer program, you can compute the dual of the fishing constraint using Lagrangian duality; and
2. If you have pure binary state variables, then cuts constructed from the Lagrangian duals result in an optimal policy.

However, these two points are quite independent. If you have integer or continuous state variables, you can still use Lagrangian duality!

The new system is more flexible because the duality handler is a property of the solution process, not the model. This allows us to use Lagrangian duality to solve any dual problem, and it leaves the decision of binarizing the state variables up to the user. (Hint: we don't think you should do it!)

Other additions

We also added support for strengthened Benders cuts, which we call SDDP.StrengthenedConicDuality.

Future plans

We have a number of future plans in the works, including better Lagrangian solution methods and better ways of integrating the different types of duality handlers (e.g., start with SDDP.ContinuousConicDuality, then shift to SDDP.StrengthenedConicDuality, then SDDP.LagrangianDuality).

If these sorts of things interest you, the code is now much more hackable, so please reach out or read Issue #246.

Alternatively, if you have interesting examples using SDDiP that you find are too slow, please send me the examples so we can use them as benchmarks in future improvements.