基于梯度投影的广义滤子填充函数方法  

A GENERALIZED FILTER FILLED FUNCTION METHOD BASED ON GRADIENT PROJECTION

作　　者：张慧雯 王薇[1] 李民[1] 徐以汎[2] ZHANG Hui-wen;WANG Wei;LI Min;XU Yi-fan(Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;School of Management, Fudan University, Shanghai 200433, China)

机构地区：[1]华东理工大学数学系,上海200237 [2]复旦大学管理学院,上海200433

出　　处：《数学杂志》2019年第1期29-41,共13页Journal of Mathematics

基　　金：国家自然科学基金(71372113)

摘　　要：本文研究了约束非凸全局优化问题.利用滤子技术和填充函数的架构,提出了一个基于梯度投影的广义滤子填充函数算法,获得了较好的理论性质和数值效果.文章修改了填充函数的定义以及滤子技术的适用范围,推广了局部优化技术,使之成为约束全局问题的有效求解方法之一.In this paper, non-convex global optimization problems with constraints are studied. By using the structures of filter and filled function, a generalized filter filled function algorithm based on gradient projection is presented and the theoretical properties and numerical results are obtained. The algorithm modifies the definition of the filled function and the application scope of the filter technique, which extends the local optimization technique and makes it one of effective methods to solve the global optimization problems with constraints.

关 键 词：非凸全局优化 约束函数 填充函数 三维滤子 

分 类 号：O221.2[理学—运筹学与控制论]