# Optimal

### From Glossary

For a mathematical program in standard form,
(the domain) is an *optimal solution* if it is a maximum (or a minimum):

- is feasible;
- for all feasible (maximum value).

Some authors refer to an optimal solution when they mean a local optimum; others mean a member of the optimality region (which are global optima). In either case, the *optimal value* is the objective value, evaluated at an optimal solution. A solution is ** nearly optimal** if it is feasible, but the optimality condition (2) is replaced by

where ( corresponds to being optimal). Typically, is specified as a small fraction, such as a cut-off tolerance for an algorithm to terminate finitely.