6 citations · 7 across the 5 of their papers we have counts for
5 papers
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…
A new finite element method for elliptic optimal control problems with pointwise state constraints in energy spaces
Wei Gong, Zhiyu Tan
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Diri…
On Lagrange multipliers of constrained optimization in Hilbert spaces
Zhiyu Tan
In this paper we introduce the essential Lagrange multiplier and establish the solid mathematical foundation of constrained optimization in Hilbert spaces with sharp results on the…
Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints
Sijing Liu, Zhiyu Tan, Yi Zhang
We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We…
Convergence analysis of the Schwarz alternating method for unconstrained elliptic optimal control problems
Wei Gong, Felix Kwok, Zhiyu Tan
In this paper we analyze the Schwarz alternating method for unconstrained elliptic optimal control problems. We discuss the convergence properties of the method in the continuous c…