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math.OC2021
The Augmented Lagrangian Method Can Approximately Solve Convex Optimization with Least Constraint Violation
Yu-Hong Dai, Liwei Zhang
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constra…
math.OC2021
Stability for Constrained Minimax Optimization
Yu-Hong Dai, Liwei Zhang
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stabili…
math.NA2021
Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals
Xiaoying Dai, Liwei Zhang, Aihui Zhou
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose…