数学最优化是以数学的方式来刻画和找出问题最优解的一门学科.机器学习利用数据构造预测方法,并对这些方法进行研究.介绍了机器学习中与支持向量机和稀疏重构相关的最优化模型.在此基础上,给出了三个典型最优化模型的对偶问题,并详细地讨论了对偶在求解这些问题中的应用. Mathematical optimization is a discipline to describe and find the optimal solution of the problem by using mathematical methods.M machine learning uses data to construct prediction methods, and studies these methods.Analyzing the relationship between machine learning and support vector machines and sparse refactoring Based on which the duality problems of three typical optimization models are given and the application of duality in solving these problems is discussed in detail.