arXiv subjects

Jimyeong Kim

Publications and source records attributed to Jimyeong Kim.

21 records · Page 2Linked to original sources

arXiv2021

Gradient-push algorithm for distributed optimization with event-triggered communications

Decentralized optimization problems consist of multiple agents connected by a network. The agents have each local cost function, and the goal is to minimize the sum of the functions cooperatively. It requires the agents communicate with each other, and reducing the cost for communication is desired for a communication-limited environment. In this work, we propose a gradient-push algorithm involving event-triggered communication on directed network. Each agent sends its state information to its neighbors only when the difference between the latest sent state and the current state is larger than a threshold. The convergence of the algorithm is established under a decay and a summability condition on a stepsize and a triggering threshold. Numerical experiments are presented to support the effectiveness and the convergence results of the algorithm.

math.OC↗

arXiv2020

Lower bounds on the radius of spatial analyticity for the Kawahara equation

In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation $u_t + uu_x + αu_{xxx} + βu_{xxxxx} = 0$, $β\neq0$, given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ can decay no faster than $1/|t|$ as $|t|\rightarrow\infty$.

math.AP↗

arXiv2019

On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations $iu_t + Δu = |u|^{p-1}u$, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ cannot decay faster than $1/|t|$ as $|t|\rightarrow\infty$. This extends the previous work of Tesfahun for the cubic case $p=3$ to the cases where $p$ is any odd integer greater than $3$.

math.AP↗