2,002 research outputs found
Proximal Stochastic Newton-type Gradient Descent Methods for Minimizing Regularized Finite Sums
In this work, we generalized and unified recent two completely different
works of Jascha \cite{sohl2014fast} and Lee \cite{lee2012proximal} respectively
into one by proposing the \textbf{prox}imal s\textbf{to}chastic
\textbf{N}ewton-type gradient (PROXTONE) method for optimizing the sums of two
convex functions: one is the average of a huge number of smooth convex
functions, and the other is a non-smooth convex function. While a set of
recently proposed proximal stochastic gradient methods, include MISO,
Prox-SDCA, Prox-SVRG, and SAG, converge at linear rates, the PROXTONE
incorporates second order information to obtain stronger convergence results,
that it achieves a linear convergence rate not only in the value of the
objective function, but also in the \emph{solution}. The proof is simple and
intuitive, and the results and technique can be served as a initiate for the
research on the proximal stochastic methods that employ second order
information.Comment: arXiv admin note: text overlap with arXiv:1309.2388, arXiv:1403.4699
by other author
Superconductivity near Itinerant Ferromagnetic Quantum Criticality
Superconductivity mediated by spin fluctuations in weak and nearly
ferromagnetic metals is studied close to the zero-temperature magnetic
transition. We solve analytically the Eliashberg equations for p-wave pairing
and obtain the normal state quasiparticle self-energy and the superconducting
transition temperature as a function of the distance to the quantum
critical point. We show that the reduction of quasiparticle coherence and
life-time due to scattering by quasistatic spin fluctuations is the dominant
pair-breaking process, which leads to a rapid suppression of to a nonzero
value near the quantum critical point. We point out the differences and the
similarities of the problem to that of the theory of superconductivity in the
presence of paramagnetic impurities.Comment: 4 pages, 1 figure, revised version to appear in Phys. Rev. Let
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