6 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…
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…
Prox-PINNs: A Deep Learning Algorithmic Framework for Elliptic Variational Inequalities
Yu Gao, Yongcun Song, Zhiyu Tan +2
Elliptic variational inequalities (EVIs) present significant challenges in numerical computation due to their inherent non-smoothness, nonlinearity, and inequality formulations. Tr…
Deep Neural ODE Operator Networks for PDEs
Ziqian Li, Kang Liu, Yongcun Song +2
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often o…
An Operator Learning Approach to Nonsmooth Optimal Control of Nonlinear PDEs
Yongcun Song, Xiaoming Yuan, Hangrui Yue +1
Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and non…
A Single-Loop Stochastic Proximal Quasi-Newton Method for Large-Scale Nonsmooth Convex Optimization
Yongcun Song, Zimeng Wang, Xiaoming Yuan +1
We propose a new stochastic proximal quasi-Newton method for minimizing the sum of two convex functions in the particular context that one of the functions is the average of a larg…