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Orbital minimization method with ℓ1 regularization
Abstract
© 2017 Elsevier Inc.We consider a modification of the orbital minimization method
(OMM) energy functional which contains an ℓ1 penalty term in order to find a sparse
representation of the low-lying eigenspace of self-adjoint operators. We analyze the
local minima of the modified functional as well as the convergence of the modified
functional to the original functional. Algorithms combining soft thresholding with
gradient descent are proposed for minimizing this new functional. Numerical tests
validate our approach. In addition, we also prove the unanticipated and remarkable
property that every local minimum of the OMM functional without the ℓ1 term is also
a global minimum.
Type
Journal articlePermalink
https://hdl.handle.net/10161/14109Published Version (Please cite this version)
10.1016/j.jcp.2017.02.005Publication Info
(2017). Orbital minimization method with ℓ1 regularization. Journal of Computational Physics, 336. pp. 87-103. 10.1016/j.jcp.2017.02.005. Retrieved from https://hdl.handle.net/10161/14109.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.
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