# Generalized upper bound

A Generalized upper bound (GUB) is an upper bound constraint on a sum of variables: $LaTeX: \textstyle\sum_{j \in J} x_j \le U$. A collection of these that do not overlap (i.e., index sets $LaTeX: J$ are disjoint) comprise the foundation for the generalized upper bounding technique in linear programming. This is where the summation equation is marked in the data structure, rather than represented explicitly as a row in the LP, and the basis is handled in its reduced dimension to gain computational efficiency in both time and space.