# Benders decomposition

### From Glossary

This decomposition separates
*complicating variables*. The (original) semi-linear model is:

*Generalized Benders decomposition* considers the following
mathematical program:

Suppose this is not a convex program, but that with each fixed , the remaining mathematical program (with being the only variable) is convex. The idea is to consider

and solve , with evaluations of requiring the solution to the convex program.