# Phase I and Phase II

### From Glossary

Phase I of a mathematical program is finding a feasible solution, and Phase II is entered with a feasible solution to find an optimal solution. The standard Phase I is:

Then, for any one could set
to have a feasible solution to the Phase I mathematical program. The optimal objective value is 0 if, and only if, and in which case is feasible in the original mathematical program (to commence Phase II). The Phase I problem is sometimes called an *elastic program* (thinking of the artificial variables as providing "elastic" behavior in the levels of constraint violation).

In linear programming, the standard Phase I & II are:

- I. Min ev: and
- II. Max cx: