中文摘要：

支持向量机是数据挖掘的新方法。支持向量机所对应的优化问题解的二阶充分条件是研究其灵敏度分析的重要基础。很弱的假设对于作为其特例的线性可分支持向量机问题一定成立，线性可分支持向量机问题解一定具有强二阶充分条件的性质；在这个假设条件下，线性支持向量分类机问题的解具有二阶充分条件性质。研究表明线性支持向量分类机问题的解在很大程度上具有二阶充分条件的性质。

英文摘要：

Support Vector Machines （SVM） is a new method for data mining. Second order sufficient condition is the basis for its optimal problem sensitivity analysis. Strong second order sufficient condition property of linear support vector classification is proposed. The hypothesis is so weak that linearly separable support vector classification meets it. The support vector classification solution is usually solved under such a hypothesis. In addition, another hypothesis is proposed for second order sufficient condition. The theories show that linear support vector classification satisfies second order sufficient condition property to a great degree.