一种非单调滤子信赖域算法解线性不等式约束优化

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一种非单调滤子信赖域算法解线性不等式约束优化王珏钰¹, 顾超¹, 朱德通²1 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 A Nonmonotone Filter-trust-region Algorithm for Linear Inequality Constrained Optimization Jue Yu WANG¹, Chao GU¹, De Tong ZHU²1 School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China;
2 Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

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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.

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收稿日期: 2019-09-14

MR (2010):

O221.2

基金资助: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****培养计划

通讯作者:顾超E-mail: guchao@lixin.edu.cn

作者简介: 王珏钰,E-mail:shnu201005@hotmail.com;朱德通,E-mail:dtzhu@shnu.edu.cn

引用本文:

王珏钰, 顾超, 朱德通. 一种非单调滤子信赖域算法解线性不等式约束优化[J]. 数学学报, 2020, 63(6): 601-620. Jue Yu WANG, Chao GU, De Tong ZHU. A Nonmonotone Filter-trust-region Algorithm for Linear Inequality Constrained Optimization. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 601-620.

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http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I6/601

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