一种非单调滤子信赖域算法解线性不等式约束优化  

A Nonmonotone Filter-trust-region Algorithm for Linear Inequality Constrained Optimization

作　　者：王珏钰 顾超 朱德通[2] Jue Yu WANG;Chao GU;De Tong ZHU(Shanghai Lixin University of Accounting and Finance,Shanghai 201209,P.R.China;Department of Mathematics,Shanghai Normal University,Shanghai 200234,P.R.China)

机构地区：[1]上海立信会计金融学院统计与数学学院,上海201209 [2]上海师范大学数学系,上海200234

出　　处：《数学学报（中文版）》2020年第6期601-620,共20页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971302);上海立信会计金融学院序伦学者培养计划。

摘　　要：本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子,并且与信赖域半径有关.当信赖域半径充分小时,新的滤子能接受试探点,避免算法无限循环.非单调信赖域策略保证了新算法的整体收敛性.目前为止,多维滤子算法局部收敛性分析仍然没有解决,在合理假设下,我们分析了新算法的局部超线性收敛性.数值结果验证了算法的有效性.We propose a new multidimensional filter algorithm with a nonmonotone trust-region strategy for linear inequality constrained optimization.The objective function and the components of its projection gradient constitute a new multidimensional filter which is related to the trust-region radius.When the trust-region radius is small enough,the new filter can accept the trial point to avoid the infinite cycle of the algorithm.The nonmonotone trust-region strategy maintains global convergence of the new algorithm.The analysis of local convergence on multidimensional filter algorithms is a problem that has not been solved so far.We analyze the local superlinear convergence of the new algorithm under some suitable conditions.Numerical results show that the new approach is efficient.

关 键 词：线性不等式约束优化 多维滤子 非单调信赖域策略 局部收敛性 

分 类 号：O122.2[理学—数学]