6 papers
Fast primal-dual methods for convex-concave bilinear saddle point problems: continuous-time dynamics and discrete algorithms
Xin He, Ya-Ping Fang
This paper studies Nesterov accelerated methods for continuously differentiable convex-concave bilinear saddle point problems. For the continuous-time model, we analyze a second-or…
Convergence of iterates and improved rates for accelerated augmented Lagrangian methods for linearly constrained convex optimization
Xin He, Nan-Jing Huang, Yi-Bin Xiao +1
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters…
Trajectory convergence and rates for Nesterov accelerated primal-dual dynamics without Lipschitz gradient assumption
Xin He, Nan-Jing Huang, Yi-Bin Xiao +1
We consider the Nesterov accelerated primal-dual dynamical system \[ \begin{cases} \ddot{x}(t)+\dfracα{t}\dot{x}(t) +\nabla f(x(t)) +A^\top\bigl(λ(t)+θt\dotλ(t)\bigr)+βA^\top(…
Safe Data-Driven Control and Dynamical Learning via Constrained Neural Architectures and Koopman Operators
Lin Feng, Xin He
The deployment of learning-based models in safety-critical control systems demands mathematical guarantees that standard regression architectures cannot provide. This paper present…
LLM Agents Make Collective Belief Dynamics Programmable: Challenges and Research Directions
Xin He, Junxi Shen, Yuchen Mou +4
Classical models of opinion dynamics assume human participants with bounded rationality and limited coordination. The rise of LLM-based agents introduces a qualitative shift: agent…
Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
Xin He, Ya-Ping Fang
In this paper, we study a bilinear saddle point problem of the form , where and are - and -strongly convex f…