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
Key words
low rank density matrix/majorized penalty algorithm/least squares problem
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