9 papers
Optimization on Affine-Transversal Hilbert Submanifolds: Part I -- Theoretical Foundations
Yongcun Song, Luhao Xue, Xiaoming Yuan +1
In this paper, we establish the theoretical foundations for the generic optimization problem in a Hilbert space whose feasible set is an affine-transversal Hilbert submanifold give…
Beyond Static Evaluation: Co-Evolutionary Mechanisms for LLM-Driven Strategy Evolution in Adversarial Games
Haoran Li, Zengle Ge, Ziyang Zhang +10
Recent advances in LLM-driven code evolution have enabled automated discovery by iteratively generating and improving programs. However, applying these methods to adversarial multi…
Stochastic Gradient Descent with Momentum is Algorithmically Stable
Yunwen Lei, Zimeng Wang, Xiaoming Yuan
Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensi…
Learning Theory of the SVRG: Generalization and Convergence Analysis
Yunwen Lei, Zimeng Wang, Xiaoming Yuan
Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learni…
A Blueprint for Self-Evolving Coding Agents in Vehicle Aerodynamic Drag Prediction
Jinhui Ren, Huaiming Li, Yabin Liu +9
High-fidelity vehicle drag evaluation is constrained less by solver runtime than by workflow friction: geometry cleanup, meshing retries, queue contention, and reproducibility fail…
Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs
Yongcun Song, Xiaoming Yuan, Hangrui Yue +1
We propose an optimization-informed deep neural network approach, named iUzawa-Net, aiming for the first solver that enables real-time solutions for a class of nonsmooth optimal co…