基于数值实验的邻近点算法收敛速度研究  

Research on Convergence Speed of Proximity Point Algorithm Based on Numerical Experiment

作　　者：王从徐 WANG Cong-xu(Department of Education,Chuzhou City Vocation College,Chuzhou,Anhui 239000,China)

机构地区：[1]滁州城市职业学院教育系,安徽滁州239000

出　　处：《石家庄学院学报》2022年第3期68-72,共5页Journal of Shijiazhuang University

基　　金：安徽省高等学校人文社会科学重点研究项目(SK2021A0978)。

摘　　要：邻近点算法是一种求解最优化问题的高效迭代算法,特别适合求解具有特殊结构的优化问题,但传统研究多基于理论分析.以二次规划问题和基追踪问题为研究对象,从数值实验角度来研究此算法的收敛速度,并应用MATLAB软件分析算法在不同的参数设置、不同的实验问题下收敛速度的变化.结果表明:在求解无约束二次规划优化问题中,r改善了目标函数的条件数,但会增加计算步骤;在求解基追踪问题中,收敛速度与步长呈正相关关系.Proximity point algorithm is an efficient iterative algorithm for solving optimization problems.It is es-pecially suitable for solving optimization problems with special structures.However,traditional research is mostly based on theoretical analysis.Taking the quadratic programming problem and the basis tracking problem as the re-search objects,the convergence rate of this algorithm is studied from the perspective of numerical experiments,and MATLAB software is used to analyze the changes in the convergence rate of the algorithm under different parameter settings and different experimental problems.The results show that in solving the unconstrained quadratic program-ming optimization problem,r improves the condition number of the objective function,but it will increase the calcu-lation steps;in solving the basis tracking problem,the convergence rate is positively correlated with the step size.

关 键 词：邻近点算法 最优化问题 二次规划 收敛速度 

分 类 号：O224[理学—运筹学与控制论]