坐标下降算法的教学实践与探索

Teaching Practice and Exploration of Coordinate Descent Algorithm

摘要: 本文以坐标下降法的教学实践为主线，系统阐述了从基础理论到跨学科应用的完整教学设计。首先，通过递进式案例解析坐标下降法的核心计算过程，突出分治优化与即时更新的本质；其次，深入探讨指标选取策略对收敛速度的影响，结合可视化对比实验，比较各自特点；最后，以机械臂运动学为应用背景，将算法拓展至非线性方程组的求解，展示数学工具解决复杂工程问题的完整路径。本研究为优化算法类课程提供了以问题驱动和实践赋能的教学范式，其方法可推广至其他数值计算课程。

Abstract: This paper develops a complete teaching framework for the coordinate descent method, spanning fundamental theory to interdisciplinary applications. The study analyzes the algorithm’s core computation through progressive case studies, highlighting its divide-and-conquer optimization and immediate update features. Secondly, the study delves into the impact of indicator selection strategies on convergence speed. By conducting visual comparative experiments, the characteristics of each strategy are analyzed and compared. Finally, taking the kinematics of robotic arms as the application background, the algorithm is extended to the solution of nonlinear equation systems, demonstrating the complete pathway for mathematical tools to solve complex engineering problems. This study provides a problem-driven and practice-empowered teaching paradigm for optimization algorithm courses, and its methods can be generalized to other numerical computation courses.