We discuss an enhancement of the Balas-Jeroslow procedure for strengthening disjunctive cuts for mixed 0-1 programs. It is based on the paradox that sometimes weakening a disjunction helps the strengthening procedure and results in sharper cuts. When applied to a split cut derived from a source row of the simplex tableau, the enhanced procedure yields, besides the Gomory Mixed Integer cut (GMI)...

Hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small size. In this paper, we propose a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs. When used iteratively, this scheme improves...

Recently, Balas and Qualizza introduced a new cut for mixed 0,1 programs, called lopsided cut. Here we present a family of cuts that comprises the Gomory mixed integer cut at one extreme and the lopsided cut at the other. We show that every inequality in this family is extreme for the appropriate infinite relaxation. We also show that these inequalities are split cuts. Finally we provide comput...

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramping constraints, time-dependent start-up costs, and start-up/shut-down ramping. To develop this perfect formulation we extend the result of Balas on unions of polyhedra to present ...