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math.NA2023
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…
math.OC2023
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…
math.NA2023★ 6 cited
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…