2 citations · 4 across the 6 of their papers we have counts for
7 papers
Derivative-free global minimization for a class of multiple minima problems
Xiaopeng Luo, Xin Xu, Daoyi Dong
We prove that the finite-difference based derivative-free descent (FD-DFD) methods have a capability to find the global minima for a class of multiple minima problems. Our main res…
A New Accelerated Stochastic Gradient Method with Momentum
Liang Liu, Xiaopeng Luo
In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse pro…
Can speed up the convergence rate of stochastic gradient methods to by a gradient averaging strategy?
Xin Xu, Xiaopeng Luo
In this paper we consider the question of whether it is possible to apply a gradient averaging strategy to improve on the sublinear convergence rates without any increase in storag…
Stochastic gradient-free descents
Xiaopeng Luo, Xin Xu
In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic d…
Numerical meshless solution of high-dimensional sine-Gordon equations via Fourier HDMR-HC approximation
Xin Xu, Xiaopeng Luo, Herschel Rabitz
In this paper, an implicit time stepping meshless scheme is proposed to find the numerical solution of high-dimensional sine-Gordon equations (SGEs) by combining the high dimension…
Meshless Hermite-HDMR finite difference method for high-dimensional Dirichlet problems
Xiaopeng Luo, Xin Xu, Herschel Rabitz
In this paper, a meshless Hermite-HDMR finite difference method is proposed to solve high-dimensional Dirichlet problems. The approach is based on the local Hermite-HDMR expansion…