Xiaole Guo | Searcharxiv

arXiv2026

Primal-dual dynamics featuring Hessian-driven damping and variable mass for convex optimization problems

This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several time-dependent parameters: variable mass, slow viscous damping, extrapolation, and temporal scaling. By employing the Lyapunov analysis approach, we obtain the strong convergence of the trajectory generated by the proposed system to the minimal norm solution of the optimization problem, as well as convergence rate results for the primal-dual gap, the objective residual, and the feasibility violation. We also show that the convergence rates of the primal-dual gap, the objective residual, and the feasibility violation can be improved by appropriately adjusting these parameters. Further, we conduct numerical experiments to demonstrate the effectiveness of the theoretical results.

math.OC↗

arXiv2025

OpenCUA: Open Foundations for Computer-Use Agents

Vision-language models have demonstrated impressive capabilities as computer-use agents (CUAs) capable of automating diverse computer tasks. As their commercial potential grows, critical details of the most capable CUA systems remain closed. As these agents will increasingly mediate digital interactions and execute consequential decisions on our behalf, the research community needs access to open CUA frameworks to study their capabilities, limitations, and risks. To bridge this gap, we propose OpenCUA, a comprehensive open-source framework for scaling CUA data and foundation models. Our framework consists of: (1) an annotation infrastructure that seamlessly captures human computer-use demonstrations; (2) AgentNet, the first large-scale computer-use task dataset spanning 3 operating systems and 200+ applications and websites; (3) a scalable pipeline that transforms demonstrations into state-action pairs with reflective long Chain-of-Thought reasoning that sustain robust performance gains as data scales. Our end-to-end agent models demonstrate strong performance across CUA benchmarks. In particular, OpenCUA-72B achieves an average success rate of 45.0% on OSWorld-Verified, establishing a new state-of-the-art (SOTA) among open-source models. Further analysis confirms that our approach generalizes well across domains and benefits significantly from increased test-time computation. We release our annotation tool, datasets, code, and models to build open foundations for further CUA research.

cs.AI↗