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math.OC2025
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…
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…