求解低秩密度矩阵约束最小二乘问题的优函数罚方法  

Majorized penalty algorithm for the least squares problem with the low rank density matrix constraint

作　　者：罗曦 熊贤祝 刘勇进 LUO Xi;XIONG Xianzhu;LIU Yongjin(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China;Fuzhou University Zhicheng College,Fuzhou,Fujian 350002,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108 [2]福州大学至诚学院,福建福州350002

出　　处：《福州大学学报（自然科学版）》2024年第2期127-133,共7页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11871153,12271097);福建省自然科学基金资助项目(2022J01103)。

摘　　要：应用优函数罚方法求解具有低秩密度矩阵约束的最小二乘问题.首先,用凸差方法处理非凸的低秩约束,并结合罚方法和优函数方法将原问题转化为一系列具有密度矩阵约束的凸优化问题;然后,给出求解该优化问题的优函数罚方法,并对该方法进行收敛性分析;最后,运用半光滑牛顿增广拉格朗日算法求解优函数罚方法的子问题.合成数据集和真实数据集上的数值结果表明,优函数罚方法可有效求解具有低秩密度矩阵约束的最小二乘问题.A majorized penalty algorithm was proposed to solve the least squares problem with the low rank density matrix constraint.We first used the difference of convex function to deal with the low rank constraint and then proposed the majorization approach to the penalized problem by solving a sequence of convex optimization without the rank constraint.Then the algorithm framework and convergence of the majorized penalty algorithm was given and analyzed.The subproblem was solved by a recently developed semismooth Newton-based augmented Lagrangian method.The experimental results on the synthetic dataset and the real dataset demonstrated the efficiency of our approach on the least squares problem with the low rank density matrix constraint.

关 键 词：低秩密度矩阵 优函数罚方法 最小二乘问题 

分 类 号：O224[理学—运筹学与控制论]