8 papers
Accelerated primal--dual dynamics and algorithms for convex optimization with nonlinear inequality constraints
Xin He
We consider convex optimization with nonlinear inequality constraints and develop a primal--dual multiplier framework that is consistent in continuous and discrete time. We first p…
A unified continuous-discrete framework for Nesterov acceleration: transitions between convex and strongly convex regimes
Xin He, Ya-Ping Fang
Classical Nesterov acceleration employs different choices of damping and inertial parameters in the convex and strongly convex settings, both for continuous-time dynamics and for d…
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(Ax(t)…
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…