2 citations · 5 across the 9 of their papers we have counts for
9 papers
Regularized Barzilai-Borwein method
Congpei An, Xin Xu
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize…
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…
Asymptotic proximal point methods: finding the global minima with linear convergence for a class of multiple minima problems
Xiaopeng Luo, Xin Xu, Herschel A. Rabitz
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. Th…
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…
Contraction methods for continuous optimization
Xiaopeng Luo, Xin Xu
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framewor…
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…
Sparse residual tree and forest
Xin Xu, Xiaopeng Luo
Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is…