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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…
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…
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…
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach
Yongcun Song, Xiaoming Yuan, Hangrui Yue
We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for a general class of nonsmooth partial differenti…