DENSITY MATRIX MINIMIZATION WITH l1 REGULARIZATION

被引：8

作者：

Lai, Rongjie ^{[1
]}

Lu, Jianfeng ^{[2
,3
,4
]}

Osher, Stanley ^{[5
,6
]}

机构：

[1] Rensselaer Polytech Inst, Dept Math, Troy, NY 12180 USA

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

[3] Duke Univ, Dept Phys, Durham, NC 27708 USA

[4] Duke Univ, Dept Chem, Durham, NC 27708 USA

[5] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[6] Univ Calif Los Angeles, Inst Pure & Appl Math, Los Angeles, CA 90095 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2015年 / 13卷 / 08期

基金：

美国国家科学基金会;

关键词：

Density matrix; l(1) regularization; eigenspace; GENERALIZED WANNIER FUNCTIONS; EXISTENCE; BLOCH;

D O I：

10.4310/CMS.2015.v13.n8.a6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm with l(1) regularization. The minimization problem can be efficiently solved by a split Bregman iteration type algorithm. We further prove that from any initial condition, the algorithm converges to a minimizer of the variational principle.

引用

页码：2097 / 2117

页数：21

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