5 citations · 7 across the 7 of their papers we have counts for
7 papers
Convergence result for the gradient-push algorithm and its application to boost up the Push-DIging algorithm
Hyogi Choi, Woocheol Choi, Gwangil Kim
The gradient-push algorithm is a fundamental algorithm for the distributed optimization problem \begin{equation} \min_{x \in \mathbb{R}^d} f(x) = \sum_{j=1}^n f_j (x), \end{equatio…
Inexact Online Proximal Mirror Descent for time-varying composite optimization
Woocheol Choi, Myeong-Su Lee, Seok-Bae Yun
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involv…
A tight bound on the stepsize of the decentralized gradient descent
Woocheol Choi
In this paper, we consider the decentralized gradinet descent (DGD) given by \begin{equation*} x_i (t+1) = \sum_{j=1}^m w_{ij} x_j (t) - α(t) \nabla f_i (x_i (t)). \end{equation*}…
mapping properties for nonlocal Schrödinger operators with certain potential
Woocheol Choi, Yong-Cheol Kim
In this paper, we consider nonlocal Schrödinger equations with certain potentials given by an integro-differential operator as follows; \begin{equation*}L_K u+V u=f\,\,\t…
The Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with certain potentials
Woocheol Choi, Yong-Cheol Kim
In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with nonnegative potentials $V\in L^q_{\loc}(\BR^n)$ for $q>\f{n}{2s}$ with $0<s…
Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity \[ \left(\sqrt{-\h…