A geometric approach to cut-generating functions

• 成果类型: Article; Proceedings Paper
• 署名作者: Basu, Amitabh; Conforti, Michele; Di Summa, Marco
• 署名单位: Johns Hopkins University; University of Padua
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0890-5
• 发表日期: 2015
• 页码: 153-189
• 关键词: infinite relaxation; gomory cuts; convex-sets; integer; THEOREM; inequalities; facets

摘要

The cutting-plane approach to integer programming was initiated more than 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. This line of research was left dormant for several decades until relatively recently, when a paper of Andersen, Louveaux, Weismantel and Wolsey generated renewed interest in the corner polyhedron and intersection cuts. Recent developments rely on tools drawn from convex analysis, geometry and number theory, and constitute an elegant bridge between these areas and integer programming. We survey these results and highlight recent breakthroughs in this area.