Orbital minimization method with ℓ1 regularization


Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Lu, J; Thicke, K

Published Date

  • May 1, 2017

Published In

Volume / Issue

  • 336 /

Start / End Page

  • 87 - 103

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/j.jcp.2017.02.005

Citation Source

  • Scopus