56 citations · 89 across the 15 of their papers we have counts for
6 papers · 1 filter
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…