5 papers
Nesterov Acceleration with Operator Decomposition
Jaewook Lee, Ernest K. Ryu, Chulhee Yun
We propose Nesterov acceleration with Operator Decomposition (NOD), which extends Nesterov's accelerated gradient descent (NAG) from smooth strongly convex optimization to the broa…
Nesterov Flow May Travel Infinitely Long to Converge to a Minimizer
Ernest K. Ryu
Recent work has established that the trajectory of the Nesterov ODE, a the continuous-time model of Nesterov's accelerated gradient method, exhibits point convergence towards a min…
ALiA: Adaptive Linearized ADMM
Uijeong Jang, Kaizhao Sun, Wotao Yin +1
We propose ALiA, a novel adaptive variant of the alternating direction method of multipliers (ADMM). Specifically, ALiA is a variant of function-linearized proximal ADMM (FLiP ADMM…
Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof
Uijeong Jang, Ernest K. Ryu
The Nesterov accelerated gradient method, introduced in 1983, has been a cornerstone of optimization theory and practice. Yet the question of its point convergence had remained ope…
Sharpness-Aware Minimization Can Hallucinate Minimizers
Chanwoong Park, Uijeong Jang, Ernest K. Ryu +1
Sharpness-Aware Minimization (SAM) is widely used to seek flatter minima -- often linked to better generalization. In its standard implementation, SAM updates the current iterate u…