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math.OC2023★ 11 cited
Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case
Meixuan He, Yuqing Liang, Jinlan Liu +1
Adam is a commonly used stochastic optimization algorithm in machine learning. However, its convergence is still not fully understood, especially in the non-convex setting. This pa…
math.OC2023★ 16 cited
Convex Quaternion Optimization for Signal Processing: Theory and Applications
Shuning Sun, Qiankun Diao, Dongpo Xu +2
Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as ful…
math.OC2022★ 13 cited
Last-iterate convergence analysis of stochastic momentum methods for neural networks
Dongpo Xu, Jinlan Liu, Yinghua Lu +2
The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems in artificial neural networks. Current convergence…