最优化方法课程研究性教学之初探——拉格朗日乘子法  

Research-based Teaching of Optimization Method Course——Lagrange Multiplier Method

作　　者：孙敏 葛静 SUN Min;GE Jing(School of Mathematics and Statistics,Zaozhuang University,Zaozhuang Shandong 277160,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160

出　　处：《菏泽学院学报》2022年第2期103-108,共6页Journal of Heze University

基　　金：枣庄学院博士科研启动基金(2021BS002)。

摘　　要：拉格朗日乘子法是对拉格朗日函数实施外罚得到的一类求解约束最优化问题的有效方法.该方法尤其适合求解含线性等式约束的凸优化问题,因此其在经济管理、机器学习等领域有着广泛的应用价值.讨论了拉格朗日乘子法的层次化教学:首先给出引入拉格朗日乘子法的必要性,然后讨论所要设计算法的序列极限满足的方程,以该方程为目标反向推导出拉格朗日乘子法的迭代格式,最后给出了拉格朗日乘子法的应用案例.Lagrange multiplier method is an effective method to solve constrained optimization problems by imposing external penalty on Lagrange function.This method is especially suitable for solving convex optimization problems with linear equality constraints.Therefore,it has wide application value in the fields of business management,machine learning and so on.This paper discusses the hierarchical teaching of Lagrange multiplier method.Firstly,the necessity of introducing Lagrange multiplier method is given.Then,the equation satisfied by the sequence limit of the algorithm to be designed is discussed.Taking this equation as the goal,the iterative format of Lagrange multiplier method is deduced in reverse.Finally,an application case of Lagrange multiplier method is given.

关 键 词：约束最优化问题 拉格朗日乘子 KKT点 

分 类 号：O224[理学—运筹学与控制论] G642[理学—数学]