# Introduction

Welcome to SDDP.jl, a package for solving large convex multistage stochastic programming problems using stochastic dual dynamic programming.

SDDP.jl is built on JuMP, so it supports a number of open-source and commercial solvers, making it a powerful and flexible tool for stochastic optimization.

The implementation of the stochastic dual dynamic programming algorithm in SDDP.jl is state of the art, and it includes support for a number of advanced features not commonly found in other implementations. This includes support for:

- infinite horizon problems
- convex risk measures
- mixed-integer state and control variables
- partially observable stochastic processes.

## Installation

Install `SDDP.jl`

as follows:

```
julia> import Pkg
julia> Pkg.add("SDDP")
```

## License

`SDDP.jl`

is licensed under the MPL 2.0 license.

## Resources for getting started

There are a few ways to get started with SDDP.jl:

- Become familiar with JuMP by reading the JuMP documentation
- Read the introductory tutorial An introduction to SDDP.jl
- Browse some of the examples, such as Example: deterministic to stochastic

## Getting help

If you need help, please open a GitHub issue.

## How the documentation is structured

Having a high-level overview of how this documentation is structured will help you know where to look for certain things.

**Tutorials**contains step-by-step explanations of how to use SDDP.jl. Once you've got`SDDP.jl`

installed, start by reading An introduction to SDDP.jl.**Guides**contains "how-to" snippets that demonstrate specific topics within SDDP.jl. A good one to get started on is Debug a model.**Explanation**contains step-by-step explanations of the theory and algorithms that underpin SDDP.jl. If you want a basic understanding of the algorithm behind SDDP.jl, start with Introductory theory.**Examples**contain worked examples of various problems solved using SDDP.jl. A good one to get started on is the Hydro-thermal scheduling problem. In particular, it shows how to solve an infinite horizon problem.The

**API Reference**contains a complete list of the functions you can use in SDDP.jl. Look here if you want to know how to use a particular function.

## Citing `SDDP.jl`

If you use `SDDP.jl`

, we ask that you please cite the following:

```
@article{dowson_sddp.jl,
title = {{SDDP}.jl: a {Julia} package for stochastic dual dynamic programming},
journal = {INFORMS Journal on Computing},
author = {Dowson, O. and Kapelevich, L.},
doi = {https://doi.org/10.1287/ijoc.2020.0987},
year = {2021},
volume = {33},
issue = {1},
pages = {27-33},
}
```

Here is an earlier preprint.

If you use the infinite horizon functionality, we ask that you please cite the following:

```
@article{dowson_policy_graph,
title = {The policy graph decomposition of multistage stochastic optimization problems},
doi = {https://doi.org/10.1002/net.21932},
journal = {Networks},
author = {Dowson, O.},
volume = {76},
issue = {1},
pages = {3-23},
year = {2020}
}
```

Here is an earlier preprint.

If you use the partially observable functionality, we ask that you please cite the following:

```
@article{dowson_pomsp,
title = {Partially observable multistage stochastic programming},
doi = {https://doi.org/10.1016/j.orl.2020.06.005},
journal = {Operations Research Letters},
author = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
volume = {48},
issue = {4},
pages = {505-512},
year = {2020}
}
```

Here is an earlier preprint.

If you use the objective state functionality, we ask that you please cite the following:

```
@article{downward_objective,
title = {Stochastic dual dynamic programming with stagewise-dependent objective uncertainty},
doi = {https://doi.org/10.1016/j.orl.2019.11.002},
journal = {Operations Research Letters},
author = {Downward, A. and Dowson, O. and Baucke, R.},
volume = {48},
issue = {1},
pages = {33-39},
year = {2020}
}
```

Here is an earlier preprint.

If you use the entropic risk measure, we ask that you please cite the following:

```
@article{dowson_entropic,
title = {Incorporating convex risk measures into multistage stochastic programming algorithms},
doi = {https://doi.org/10.1007/s10479-022-04977-w},
journal = {Annals of Operations Research},
author = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
year = {2022},
}
```

Here is an earlier preprint.