A framework for generalized Benders' decomposition and its application to multilevel optimization

• 成果类型: Article
• 署名作者: Bolusani, Suresh; Ralphs, Ted K.
• 署名单位: Lehigh University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01763-7
• 发表日期: 2022
• 页码: 389-426
• 关键词: global optimization; integer; algorithm; inequalities; PROGRAMS; Knapsack; cuts

摘要

We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of optimization problems that fall under the umbrella of multilevel/multistage mixed integer linear optimization problems. The application of this abstract framework to this broad class of problems provides new insights and a broader interpretation of the core ideas, especially as they relate to duality and the value functions of optimization problems that arise in this context.