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On the Influence of Bias-Correction on Distributed Stochastic Optimization

Ali H. Sayed, Bicheng Ying, Kun Yuan, Sulaiman A S A E Alghunaim

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed deterministic optimization problems. These methods employ constant step-sizes and converge linearly to the exact ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Max-Olivier Hongler

he concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose ...

2020

An adaptive algorithm for the transport equation with time dependent velocity

Marco Picasso, Samuel Dubuis

An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

2020

Optimal Allocation of ESSs in Active Distribution Networks to achieve their Dispatchability

Mario Paolone, Sidi-Rachid Cherkaoui, Ji Hyun Yi

This paper presents a method for the optimal siting and sizing of energy storage systems (ESSs) in active distribution networks (ADNs) to achieve their dispatchability. The problem formulation accounts for the uncertainty inherent to the stochastic nature ...

IEEE Institute of Electrical and Electronics Engineers2020

On the Performance of Exact Diffusion over Adaptive Networks

Ali H. Sayed, Sulaiman A S A E Alghunaim, Bicheng Ying, Kun Yuan

Various bias-correction methods such as EXTRA, DIGing, and exact diffusion have been proposed recently to solve distributed deterministic optimization problems. These methods employ constant step-sizes and converge linearly to the exact solution under prop ...

IEEE2019

Variance-Reduced Stochastic Learning by Networked Agents Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

This paper develops a distributed variance-reduced strategy for a collection of interacting agents that are connected by a graph topology. The resulting diffusion-AVRG (where AVRG stands for "amortized variance-reduced gradient") algorithm is shown to have ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

High-Order Accurate Conservative Finite Difference Methods For Vlasov Equations In 2D+2V

Stephan Brunner

This manuscript discusses discretization of the Vlasov-Poisson system in 2D+2V phase space using high-order accurate conservative finite difference algorithms. One challenge confronting direct kinetic simulation is the significant computational cost associ ...

SIAM PUBLICATIONS2019

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