从约束优化问题的Lagrange对偶看《最优化方法》课程的驱动化教学

On the Driving Teaching of the Course of Optimizing Method from the Lagrange Duality of Constrained Optimizing Problem

摘要: 最优化理论，特别是约束优化问题的Lagrange对偶理论是《最优化方法》课程的重要内容，也是难点内容。对此，我们从约束优化问题的最优性条件入手，引出了约束优化问题的鞍点的定义，再由此引出与约束优化问题相关的两个双层极值问题，从而引出约束优化问题的Lagrange对偶规划。这样一层层驱动性地引入约束优化问题的Lagrange对偶，既降低了最优化对偶理论的教学难度，也提高了学生的学习兴趣。

Abstract: The optimization theory, especially the Lagrange duality theory of constrained optimization problems, is an important and difficult part of the course Optimizing Method. In this regard, based on the optimality conditions of constrained optimization problems, we first introduce the definition of saddle point of constrained optimization problems, and then derive two bilevel extreme value problems related to constrained optimization problems, which leads to Lagrange dual programming of constrained optimization problems. In this way, Lagrange duality of constrained optimization problem is introduced layer by layer, which not only reduces the teaching difficulty of optimization duality theory, but also arouses students’ interest in learning.