56 citations · 89 across the 15 of their papers we have counts for
16 papers
A universal accelerated primal-dual method for convex optimization problems
Hao Luo
This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and Hölder gradients b…
An efficient semismooth Newton-AMG-based inexact primal-dual algorithm for generalized transport problems
Jun Hu, Hao Luo, Zihang Zhang
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the t…
A unified differential equation solver approach for separable convex optimization: splitting, acceleration and nonergodic rate
Hao Luo, Zihang Zhang
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in t…
Accelerated primal-dual methods for linearly constrained convex optimization problems
Hao Luo
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence ra…
A Unified Convergence Analysis of First Order Convex Optimization Methods via Strong Lyapunov Functions
Long Chen, Hao Luo
We present a unified convergence analysis for first order convex optimization methods using the concept of strong Lyapunov conditions. Combining this with suitable time scaling fac…
Optimal error estimation of a time-spectral method for fractional diffusion problems with low regularity data
Hao Luo, Xiaoping Xie
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order (). The solution regularity in the Sobolev space i…
A primal-dual flow for affine constrained convex optimization
Hao Luo
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to…
Accelerated differential inclusion for convex optimization
Hao Luo
This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponenti…
First order optimization methods based on Hessian-driven Nesterov accelerated gradient flow
Long Chen, Hao Luo
A novel dynamical inertial Newton system, which is called Hessian-driven Nesterov accelerated gradient (H-NAG) flow is proposed. Convergence of the continuous trajectory are establ…
From differential equation solvers to accelerated first-order methods for convex optimization
Hao Luo, Long Chen
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynam…
Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data
Hao Luo, Binjie Li, Xiaoping Xie
This paper analyzes the convergence of a Petrov-Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the tim…
Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data
Binjie Li, Hao Luo, Xiaoping Xie
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is…
Analysis of a time-stepping scheme for time fractional diffusion problems with nonsmooth data
Binjie Li, Hao Luo, Xiaoping Xie
This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem wi…
A space-time finite element method for fractional wave problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional d…
Analysis of a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper analyzes a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems with two time fractional derivatives of orders and ($ 0 < α…
A time-spectral algorithm for fractional wave problems
Binjie Li, Hao Luo, Xiaoping Xie
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the s…