Reformulations in Mathematical Programming: Definitions

Abstract. A reformulation of a mathematical program is a formulation 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, it is desirable that reformulations can be carried out automatically. Reformulation techniques are very common in mathematical programming but interestingly they have never been studied under a common framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations, give several fundamental definitions categorizing reformulations in essentially four types (opt-reformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type.

• Type: Conference
• Year: 2008
• Where: COLOGNETWENTE
• Authors: Leo Liberti
• Keywords: Better Than, COLOGNETWENTE 2008, Mathematical Programming, Optimization, Reformulation Techniques