467 research outputs found
A Particle-Based Algorithm for Distributional Optimization on \textit{Constrained Domains} via Variational Transport and Mirror Descent
We consider the optimization problem of minimizing an objective functional,
which admits a variational form and is defined over probability distributions
on the constrained domain, which poses challenges to both theoretical analysis
and algorithmic design. Inspired by the mirror descent algorithm for
constrained optimization, we propose an iterative particle-based algorithm,
named Mirrored Variational Transport (mirrorVT), extended from the Variational
Transport framework [7] for dealing with the constrained domain. In particular,
for each iteration, mirrorVT maps particles to an unconstrained dual domain
induced by a mirror map and then approximately perform Wasserstein gradient
descent on the manifold of distributions defined over the dual space by pushing
particles. At the end of iteration, particles are mapped back to the original
constrained domain. Through simulated experiments, we demonstrate the
effectiveness of mirrorVT for minimizing the functionals over probability
distributions on the simplex- and Euclidean ball-constrained domains. We also
analyze its theoretical properties and characterize its convergence to the
global minimum of the objective functional
Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations
We propose an efficient computational method for evaluating the self-energy
matrices of electrodes to study ballistic electron transport properties in
nanoscale systems. To reduce the high computational cost incurred in large
systems, a contour integral eigensolver based on the Sakurai-Sugiura method
combined with the shifted biconjugate gradient method is developed to solve
exponential-type eigenvalue problem for complex wave vectors. A remarkable
feature of the proposed algorithm is that the numerical procedure is very
similar to that of conventional band structure calculations. We implement the
developed method in the framework of the real-space higher-order finite
difference scheme with nonlocal pseudopotentials. Numerical tests for a wide
variety of materials validate the robustness, accuracy, and efficiency of the
proposed method. As an illustration of the method, we present the electron
transport property of the free-standing silicene with the line defect
originating from the reversed buckled phases.Comment: 36 pages, 13 figures, 2 table
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