# Linearity interval

### From Glossary

When a univariate function is piece-wise linear, it has the form
for in the interval
, where is
not equal to . (The phrase usually means the function is
continuous.) This arises in linear programming when considering the
optimal value as a function of varying right-hand sides
(or cost coefficients) in fixed proportions: (or ),
where is an admissible change
vector and is the (scalar) variable. Then, for the range of
where the LP has a solution, the optimal value function has this
piece-wise linear (continuous) form, and the intervals that
comprise the domain are called *linearity intervals*.