支持向量机是一种有效的机器学习方法，但随着数据规模的增大它会消耗大量的运算时间和内存。为了克服上述问题，本项目以变分不等式和对偶投影方法为依据，构建基于safe screening的支持向量机稀疏模型及其快速求解方法。通过前一个优化问题的解，筛选出下一个优化问题解中对应值为0或1的样本，这样大大缩减了优化问题的规模，而且得到与原问题完全一致的解。包括以下内容：基于变分不等式与对偶投影的Twin支持向量机稀疏求解方法；基于safe screening的半监督支持向量机以及半监督Twin支持向量机的稀疏求解方法；构建基于safe Screening的支持向量机的多参数选择模型；构建基于支持向量机的样本与特征同时约减的safe screening模型；改进现有的支持向量机的safe screening准则；最后丰富和完善safe screening的相关理论等。

Support vector machine is an effective machine learning method, and it costs large amount of running time and storage. To address it, based on variational inequality and dual projection methods, sparse support vector machines and their safe screening rules are researched in this project. These rules can greatly reduce the scale of the optimization problems by safely discarding most samples before solving the optimization problem. Moreover we can obtain the same solution as the original optimization problem. The following main contents are included: The sparse solving methods for twin support vector machine based on variational inequality and dual projection methods. The sparse solving methods for semi-supervised support vector machine and semi-supervised twin support vector machine based on safe screening. Parameters selection for multiple parameters in SVM based on safe screening. Sample and feature selection for SVM simultaneously based on safe screening. Modified original safe screening rules for SVM. Enrich and improve the responding theory of safe screening.