支持向量机（SVM）是机器学习与人工智能领域中的一个重要研究方向，而最优化是支持向量机的核心技术，占有非常重要的地位。本项目旨在海南大学邵元海博士利用北京交通大学修乃华教授在最优化方面的研究经验，两人结对在北京交通大学共同开展海量复杂数据环境下支持向量机中不定核学习的低秩优化理论与算法研究，具体内容包括：(1)依托秩的变分性质，建立SVM不定核矩阵学习低秩优化原模型的最优性理论、对偶理论、精确罚函数理论。(2)设计求解该模型的低秩投影/Prox算法和低秩牛顿算法、使之具有快速有效性；(3)针对支持向量机中的实际问题进行数值实验，从中选取优秀的算法并开发性能优异的求解器。本项目的实施不仅能为支持向量机提供新理论和新方法，而且也可为学科交叉与融合提供实践经验，对于人才培养以及两校之间的深度合作与交流起到积极推动作用。

Support vector machine (SVM) is an important research area in machine learning and artificial intelligence, and optimization is the core technology of support vector machine, which occupies a very important position. The project aims to cooperate with Dr. Shao Yuanhai of Hainan University, and to utilize the rich research experiences of Professor Xiu Naihua in optimization from Beijing Jiaotong University, and to jointly study the low-rank optimization theory and algorithms for the SVM indefinite kernel learning under massive data environment. The contents include as follows: (1) Based on the variational properties of rank, establish the optimality theory, dual theory, and exact penalty function theory of the low-rank SVM indefinite kernel model; (2) Design the low-rank projection/Prox algorithms and low-rank Newton algorithms for the model, which are fast and effective; (3) Implement the numerical experiments of the above models and algorithms, and select excellent algorithms to develop the corresponding SVM software. This project not only provides new theories and new methods for SVM, but also provides practical experience for interdisciplinary and integration, and plays an active role in talent training and in-depth cooperation and communication between the two universities.