Gauss回代交替方向法求解一类二次规划逆问题
Gauss Back Substitution Alternating Direction Method for a Class of Inverse Quadratic Programming
DOI: 10.12677/AAM.2020.91008, PDF, HTML, 下载: 762  浏览: 3,043 
作者: 李丽丹：大连理工大学数学科学学院，辽宁 大连；辽宁工程技术大学理学院，辽宁 阜新；张宏伟, 张立卫：大连理工大学数学科学学院，辽宁 大连
关键词: 谱范数；无穷范数；二次规划；G-ADMM法；Spectrum Norm； Infinite Norm； Quadratic Programming； G-ADMM Method
摘要: 本文求解了目标函数为矩阵谱范数与向量无穷范数之和的一类二次规划的逆问题。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 Gauss 回代交替方向法求解该问题。而对于其中一个子问题的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，但无法精确求解每个变量，所以采用非精确方法求解该子问题。最后给出采用的 Gauss 回代交替方向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。
Abstract: In this paper, we solve the inverse problem of quadratic programming whose objective function is the sum of matrix spectrum norm and vector infinite norm. We transform the problem into a convex optimization problem with objective function separable and propose Gauss back substitution alternating direction method to solve it. We find that one of its subproblems is still a convex optimization problem with objective function separable, but it is impossible to solve every variable accurately. So we use the inexact method to solve the subproblem. Finally, the numerical experiment of the problem in this paper is given. The data shows that the method in this paper can solve the inverse quadratic programming problem efficiently and quickly.
文章引用：李丽丹, 张宏伟, 张立卫. Gauss回代交替方向法求解一类二次规划逆问题[J]. 应用数学进展, 2020, 9(1): 60-71. https://doi.org/10.12677/AAM.2020.91008

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