外罚函数法与广义Lagrange乘子法的比较研究  

A Comparative Study of External Penalty Function Method and Generalized Lagrangian Multiplier Method

作　　者：宋菲 吴泽忠 

机构地区：[1]成都信息工程大学应用数学学院,四川成都610225

出　　处：《成都信息工程大学学报》2017年第6期667-674,共8页Journal of Chengdu University of Information Technology

基　　金：国家自然科学基金资助项目(71672013);四川省软件科学研究计划资助项目(2014ZR0016);四川省哲学社会科学重点研究基地-系统科学与企业发展研究中心(重点)资助项目(Xq141306)

摘　　要：基于非线性约束优化问题,讨论了外罚函数法与广义Lagrange乘子法,并通过MATLAB编程实现了两种算法。实验表明:(1)广义Lagrange乘子法在迭代次数和收敛结果上优于外罚函数法且对初始点的选取要求不高;(2)广义Lagrange乘子法的罚因子的修正系数不宜过大,一般在区间(1,2)上取值,广义Lagrange乘子法更具优越性。最后,通过3个工业工程中的非线性规划实际问题说明乘子法比外罚函数法具有更广泛的实用性。Based on the nonlinear constrained optimization problem,this paper discussed the external penalty function method and the generalized lagrangian multiplier method,and two algorithms have been implemented by programming.The experimental results show that：（ 1） The generalized multiplier method is superior to the external penalty function method in the iteration times and the convergence results,and the selection of the initial point is not strict.（ 2） The correction factor of the penalty factor of the generalized multiplier method should not be too large,evaluating on the interval（ 1,2） is more superior.Finally,the practical problems of nonlinear programming in three industrial projects show that the generalized lagrangian multiplier method has more practicability than the external penalty function method.

关 键 词：约束优化 外罚函数法 广义Lagrange乘子法 罚因子 修正系数 

分 类 号：O221.2[理学—运筹学与控制论]