Orbital minimization method with ℓ<sup>1</sup> regularization
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2017-05-01
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© 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.
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Lu, J, and K Thicke (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.
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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.
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