# Restricted basis entry rule

### From Glossary

This is a restriction on which variables can enter the basis in a simplex method. A common rule arises in separable programming, which uses specially ordered sets: a group of non-negative variables must sum to 1 such that at most two variables are positive, and if two are positive, they must be adjacent. For example, suppose the variables are Then, it is feasible to have and but it is not feasible to have or In this case the rule is not to permit a variable to enter the basis unless it can do so without violating the adjacency requirement. For example, if is currently basic, would not be considered for entry.

Another restricted entry rule pertains to the delta form of separable programming (plus other applications): *Do not admit a variable into the basis unless its predecessor variables are at their upper bound.* This means there is an ordered set of bounded variables, say such that
Then, is not considered for basis entry unless for all