16 citations · 62 across the 39 of their papers we have counts for
40 papers
Non-ergodic linear convergence property of the delayed gradient descent under the strongly convexity and the Polyak-Łojasiewicz condition
Hyung Jun Choi, Woocheol Choi, Jinmyoung Seok
In this work, we establish the linear convergence estimate for the gradient descent involving the delay when the cost function is -strongly convex and -smoot…
Convergence property of the Quantized Distributed Gradient descent with constant stepsizes and an effective strategy for the stepsize selection
Woocheol Choi, Myeong-Su Lee
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance o…
On the convergence of the distributed proximal point algorithm
Woocheol Choi
In this work, we establish convergence results for the distributed proximal point algorithm (DPPA) for distributed optimization problems. We consider the problem on the whole domai…
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*}…
On the convergence result of the gradient-push algorithm on directed graphs with constant stepsize
Woocheol Choi, Doheon Kim, Seok-Bae Yun
Distributed optimization has recieved a lot of interest due to its wide applications in various fields. It consists of multiple agents that connected by a graph and optimize a tota…
On the convergence of decentralized gradient descent with diminishing stepsize, revisited
Woocheol Choi, Jimyeong Kim
Distributed optimization has received a lot of interest in recent years due to its wide applications in various fields. In this work, we revisit the convergence property of the dec…
Convergence analysis of the splitting method to the nonlinear heat equation
Hyung Jun Choi, Woocheol Choi, Youngwoo Koh
In this paper, we analyze an operator splitting scheme of the nonlinear heat equation in (): in $Ω\times(0,\infty…
Event-triggered bipartite consensus for multiagent system with general linear dynamics: an integral-type event triggered control
Nhan-Phu Chung, Thanh-Son Trinh, Woocheol Choi
In this paper, we propose an integral based event-triggering controller for bipartite consensus of the multi-agent systems whose dynamics are described by general linear system. We…
Gradient-push algorithm for distributed optimization with event-triggered communications
Jimyeong Kim, Woocheol Choi
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 function…
A unified framework for distributed optimization algorithms over time-varying directed graphs
Woocheol Choi, Doheon Kim, Seok-Bae Yun
In this paper, we propose a framework under which the decentralized optimization algorithms suggested in \cite{JKJJ,MA, NO,NO2} can be treated in a unified manner. More precisely,…
Convergence results of a nested decentralized gradient method for non-strongly convex problems
Woocheol Choi, Doheon Kim, Seok-Bae Yun
We are concerned with the convergence of NEAR-DGD (Nested Exact Alternating Recursion Distributed Gradient Descent) method introduced to solve the distributed optimization prob…
Asymptotic profile of solutions to the heat equation on thin plate with boundary heating
Eun-ho Lee, Woocheol Choi
In this section, we consider the heat equation on a plate with thickness h > 0 being heated by a heat source on upper and lower faces of the plate. We obtain an asymptotic profile…
Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation
Woocheol Choi, Younghun Hong, Jinmyoung Seok
For the gravitational Vlasov-Poisson equation, Guo and Rein constructed a class of classical isotropic states as minimizers of free energies (or energy-Casimir functionals) under m…
A sharp error analysis for the discontinuous Galerkin method of optimal control problems
Woocheol Choi, Young-Pil Choi
In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Gale…
Convergence rate of the finite element approximation for extremizers of Sobolev inequalities
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we are concerned with the convergence rate of a FEM based numerical scheme approximating extremal functions of the Sobolev inequality. We prove that when the domain…
Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola
Woocheol Choi, Seunghyeok Kim
The Lane-Emden system is written as \begin{equation*} \begin{cases} -Δu = v^p &\text{in } Ω,\\ -Δv = u^q &\text{in } Ω,\\ u, v > 0 &\text{in } Ω,\\ u = v = 0 &\text{on } \partial Ω…
Uniqueness and symmetry of ground states for higher-order equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients.…
Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results
Woocheol Choi, Raphael Ponge
In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold wit…
On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schrödinger equation $$\left( \sqrt{-c^2Δ+ m^2 c^4}-mc^2\rig…
Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates
Raphael Ponge, Woocheol Choi
This paper is a sequel of arxiv:1709.09045 and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold equipp…
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…