# Lexicographic order

### From Glossary

A nonzero vector is *lexicographically positive*
if its first non-zero coordinate is positive. The vector is
*lexicographically greater than* the vector if is
lexicographically positive, and this defines the *lexicographic
order* in This is a *total ordering* in that every two
vectors are either equal, or one is lexicographically greater than
the other.

This was first used in mathematical programming to resolve cycling in the simplex method. It also provides a way to obtain solutions for multiple objectives with the property that is a Pareto maximum if is lexicographically greater than or equal to for all feasible .