AI 中文总结
针对带二次目标函数的组合优化问题SDP松弛，提出新型面部约化原始算法，利用可行解简化步骤，平均比标准实现快4倍，改进SDP松弛预处理。
AI 中文摘要
我们提出一种专为带二次目标函数的组合优化问题半定规划（SDP）松弛设计的新型面部约化算法。该方法利用此类松弛的特定结构，尤其是实际中常可高效生成可行解的特性，将此类解融入面部约化过程，大幅简化约化步骤。在考虑的基准集上，该算法平均比标准实现快4倍，为组合优化中的SDP松弛提供显著改进的预处理。
英文摘要
We propose a novel facial reduction algorithm tailored to semidefinite programming relaxations of combinatorial optimization problems with quadratic objective functions. Our method leverages the specific structure of these relaxations, particularly the availability of feasible solutions that can often be generated efficiently in practice. By incorporating such solutions into the facial reduction process, we substantially simplify the reduction steps. On average, our facial reduction algorithm is four times faster than the standard implementation on the considered benchmark sets, providing significantly improved preprocessing for SDP relaxations in combinatorial optimization.
