李丽丹¹, 张立卫², 张宏伟²

1. 辽宁工程技术大学理学院, 阜新 123000;
2. 大连理工大学数学科学学院, 大连 116024

收稿日期:2019-11-18发布日期:2021-05-13


基金资助:国家自然科学基金（No.11971089，11731013）和辽宁省教育厅项目（No.LJ2020QNL008）资助.

A TYPE OF NON-DIFFERENTIABLE INVERSE QUADRATIC PROGRAMMING PROBLEMS

Li Lidan¹, Zhang Liwei², Zhang Hongwei²

1. College of Science, Liaoning Technical University, Fuxin 123000, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received:2019-11-18Published:2021-05-13







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本文求解了一类二次规划的逆问题，具体为目标函数是矩阵谱范数与向量无穷范数之和的最小化问题.首先将该问题转化为目标函数可分离变量的凸优化问题，提出用G-ADMM法求解.并结合奇异值阈值算法，Moreau-Yosida正则化算法，matlab优化工具箱的quadprog函数来精确求解相应的子问题.而对于其中一个子问题的精确求解过程中发现其仍是目标函数可分离变量的凸优化问题，由于其变量都是矩阵，所以采用适合多个矩阵变量的交替方向法求解，通过引入新的变量，使其每个子问题的解都具有显示表达式.最后给出采用的G-ADMM法求解本文问题的数值实验.数据表明，本文所采用的方法能够高效快速地解决该二次规划逆问题.
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