# Parametric programming

### From Glossary

Solving a family of mathematical programs over a parameter space. For example, consider the family of linear programs:

where t is a (scalar) parameter and d is a specified direction vector. Starting with the LP is solved, then an optimal basis is found (if possible) that remains optimal as is increased. The max value of is determined; if this is finite, the basis changes to a new optimal basis (for the max value) such that can be further increased, if possible. This is continued until either cannot be increased any further or a basis is found that remains optimal on the interval,
where
are the *break points* of the optimal objective value as a function of the parameter.