非光滑约束问题的既约次梯度法  

AN AGGREGATE SUBGRADIENT METHODS FOR NONSMOOTH CONSTRAINED MINIMIZATION

作　　者：谭亚[1] 庄建南[2] 

机构地区：[1]河海大学港口航道及海岸工程系,南京210098 [2]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2000年第4期325-330,共6页Numerical Mathematics A Journal of Chinese Universities

摘　　要：In this paper, by the Lagrange dual theory, the nonsmooth constrained minimization, where the objective function and the constrained functions are Lips- chitzian, can be regarded as a convex programming with linear constrains. We give the related aggregate subgradient method, and prove that either a solution of this nonsmooth constrained minimization problem can be obtained after a finite number of iterations or a sequence {xk} is generated so that each cluster point of {xk} is an optimal solution of the problem. The numerical examples show that the new method suggested here is practical and efficient.In this paper, by the Lagrange dual theory, the nonsmooth constrained minimization, where the objective function and the constrained functions are Lips- chitzian, can be regarded as a convex programming with linear constrains. We give the related aggregate subgradient method, and prove that either a solution of this nonsmooth constrained minimization problem can be obtained after a finite number of iterations or a sequence {xk} is generated so that each cluster point of {xk} is an optimal solution of the problem. The numerical examples show that the new method suggested here is practical and efficient.

关 键 词：非光滑约束问题 既约次梯度法 非线性规划 LAGRANGE对偶 

分 类 号：O221.2[理学—运筹学与控制论]