Density matrix minimization with ℓ1 regularization
Date
2015-01-01
Journal Title
Journal ISSN
Volume Title
Repository Usage Stats
views
downloads
Abstract
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 ℓ1 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.
Type
Department
Description
Provenance
Subjects
Citation
Permalink
Collections
Scholars@Duke
Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.