6,348 research outputs found
Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression
The l1-regularized logistic regression is a widely used statistical model in
data classification. This paper proposes a dual Newton method based proximal
point algorithm (PPDNA) to solve the l1-regularized logistic regression problem
with bias term. The global and local convergence of PPDNA hold under mild
conditions. The computational cost of a semismooth Newton (Ssn) algoithm for
solving subproblems in the PPDNA can be effectively reduced by fully exploiting
the second-order sparsity of the problem. We also design an adaptive sieving
(AS) strategy to generate solution paths for the l1-regularized logistic
regression problem, where each subproblem in the AS strategy is solved by the
PPDNA. This strategy exploits active set constraints to reduce the number of
variables in the problem, thereby speeding up the PPDNA for solving a series of
problems. Numerical experiments demonstrate the superior performance of the
PPDNA in comparison with some state-of-the-art second-order algorithms and the
efficiency of the AS strategy combined with the PPDNA for generating solution
paths
Interplay between Quantum Size Effect and Strain Effect on Growth of Nanoscale Metal Thin Film
We develop a theoretical framework to investigate the interplay between
quantum size effect (QSE) and strain effect on the stability of metal
nanofilms. The QSE and strain effect are shown to be coupled through the
concept of "quantum electronic stress. First-principles calculations reveal
large quantum oscillations in the surface stress of metal nanofilms as a
function of film thickness. This adds extrinsically additional strain-coupled
quantum oscillations to surface energy of strained metal nanofilms. Our theory
enables a quantitative estimation of the amount of strain in experimental
samples, and suggests strain be an important factor contributing to the
discrepancies between the existing theories and experiments
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