Reformulations in Mathematical Programming: Definitions and Systematics

A reformulation of a mathematical program is a formu- lation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, itis desirable that reformulations can be carried out automatically. Refor- mulation techniques are very common in mathematical programming but interestingly they have never been studied under a common frame- work. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical pro- gramming formulations, give several fundamental definitions categoriz- ing reformulations in essentially four types (opt-reformulations, narrow- ings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type.