7,724 research outputs found

    Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression

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    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

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    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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