Copositive Duality for Discrete Energy Markets
将电力系统机组组合问题转化为完全正规划，利用共正对偶和强对偶设计新的定价机制，确保收入充足并支持市场均衡，通过割平面算法和二阶锥近似实现高效求解。
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. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00906 .