Copositive Duality for Discrete Energy Markets

• 成果类型: Article; Early Access
• 署名作者: Guo, Cheng; Bodur, Merve; Taylor, Joshua A.
• 署名单位: Clemson University; University of Edinburgh; University of Edinburgh; Heriot Watt University; New Jersey Institute of Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.00906
• 发表日期: 2025
• 关键词: copositive programming; electricity market; pricing; Strong Duality; unit commitment

摘要

Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. We apply this perspective by writing unit commitment in power systems as a completely positive program and then using the dual copositive program and strong duality to design new pricing mechanisms. We show that the mechanisms are revenue-adequate and, under certain conditions, support a market equilibrium. To facilitate implementation, we also employ a cutting plane algorithm for solving copositive programs exactly, which we further speed up via a second-order cone programming approximation. We provide numerical examples to illustrate the potential benefits of the pricing mechanisms and algorithms.