AI 中文总结
该研究针对二元指示项控制连续变量的混合整数凸优化问题，提出CORe框架，通过融入逐坐标最优性信息提升分支定界性能，经实验验证其较标准big-M重构可大幅优化求解器表现。
AI 中文摘要
我们研究二元指示项控制连续变量的混合整数凸优化问题。我们提出了坐标最优性重构（Coordinate Optimality Reformulation, CORe）框架，该框架通过融入逐坐标最优性信息来增强标准指示项重构。所得重构保留全局最优性，同时大幅提升分支定界性能，尤其在稀疏和结构化场景中，逐坐标最优性条件可揭示可利用的问题结构。我们首先开发CORe的核心组件，包括逐坐标最优性条件、闭式表征和析取重构；随后在二次问题、鲁棒单指数模型等多个问题族中验证该框架。计算实验表明，与标准大M（big-M）重构相比，CORe可大幅提升求解器性能。
英文摘要
We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the \emph{Coordinate Optimality Reformulation} (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable problem structure. We first develop the main components of CORe, including coordinate-wise optimality conditions, closed-form characterizations, and disjunctive reformulations. We then demonstrate the framework across multiple problem families, including quadratic problems and robust single-index models. Computational experiments show that CORe can substantially improve solver performance compared with standard big-$M$ formulations.
