一类求解非线性约束优化问题的线搜索渐缩滤子算法  

A Line Search Method with Dwindling Filter Technique for Solving Nonlinear Constrained Optimization

作　　者：裴永刚 孔维悦 董兰婷 PEI Yonggang;KONG Weiyue;DONG Lanting(Engineering Laboratovy for Big Data Statistical Analysis and Optimal Control,College of Mathematics and Information Science,Henan Normal Universitgy,Xinariang 453000,China)

机构地区：[1]河南师范大学数学与信息科学学院大数据统计分析与优化控制河南省工程实验室,河南新乡453000

出　　处：《应用数学》2021年第3期543-557,共15页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(12071133,11801152);the Key Scientific Research Project for Colleges and Universities in Henan Province(21A110012)。

摘　　要：针对非线性等式约束优化问题,本文给出一种新的线搜索滤子算法.算法中将非线性等式约束优化问题的最优性条件作为滤子,并在接受准则中加入渐缩函数,使得当线搜索试探步长减小时时滤子包络的越来越薄,从而使得试探步被接受程度更有弹性,不会被当前的迭代点拒绝.在适当的假设下,证明算法的全局收敛性,并给出算法初步的数值实验结果.In this paper,a different line search filter algorithm is proposed for solving nonlinear equality constrained optimization.The optimality condition of the nonlinear optimization problem is regarded as a new filter pair which is embedded in the backtracking line search framework.By adding a dwindling function to the step acceptance criteria,the thickness of the filter’s envelope is getting smaller and smaller when the step size decreases.So the line search trial step size in becomes more flexible to accept.And the dwindling filter do not make the trial step be denied by current iteration point.Under some reasonable assumptions,the global convergence of the algorithm is proved.Some preliminary numerical experiment results are reported.

关 键 词：非线性约束优化 线搜索 渐缩滤子方法 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]