一个线性约束优化问题的广义梯度投影法(英文)  

A Superlinearly Convergent Generalized Gradient Projection Method for Nonlinear Optimization Problems with Linear Constraints

作　　者：曾庆光[1] 吴义虎[2] 郭湘德[2] 

机构地区：[1]湖南大学,长沙410082 [2]长沙理工大学,长沙410076

出　　处：《运筹学学报》2005年第4期44-48,共5页Operations Research Transactions

基　　金：This work is supported by National Natural Science Foundation of China (No.50276005) and (No. 10472016).

摘　　要：本文对线性约束优化问题提出了一个新的广义梯度投影法,该算法采用了非精确线性搜索,并在每次迭代运算中结合了广义投影矩阵和变尺度方法的思想确定其搜索方向．在通常的假设条件下,证明了该算法的整体收敛性和超线性收敛速度．In this paper, a new generalized gradient projection method with inexact line search is proposed for the nonlinear optimization problem with linear constraints. The main idea is to use the generalized projection matrix combined with the variable metric method to determine the search direction at each iteration. Under some suitable assumption it is proved that our method is of global convergence properties and superlinear convergence rate.

关 键 词：运筹学 优化问题 广义梯度投影 算法 非精确搜索 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]