Jaewook J. Suh – Optimization Online

Swapping objectives accelerates Davis-Yin splitting

Published: 2025/06/30

Convex Optimization, Nonsmooth Optimization complexity, convex optimization, Davis-Yin splitting, douglas-rachford splitting, first-order methods, proximal splitting algorithms

In this work, we investigate the application of Davis–Yin splitting (DYS) to convex optimization problems and demonstrate that swapping the roles of the two nonsmooth convex functions can result in a faster convergence rate. Such a swap typically yields a different sequence of iterates, but its impact on convergence behavior has been largely understudied or … Read more

An Adaptive and Parameter-Free Nesterov’s Accelerated Gradient Method for Convex Optimization

Published: 2025/05/16

Jaewook J. Suh

Shiqian Ma

Convex Optimization Adaptive methods, convex optimization, first-order methods, Line-Search-Free, parameter-free

We propose AdaNAG, an adaptive accelerated gradient method based on Nesterov’s accelerated gradient method. AdaNAG is line-search-free, parameter-free, and achieves the accelerated convergence rates \( f(x_k) – f_\star = \mathcal{O}\left(1/k^2\right) \) and \( \min_{i\in\left\{1,\dots, k\right\}} \|\nabla f(x_i)\|^2 = \mathcal{O}\left(1/k^3\right) \) for \( L \)-smooth convex function \( f \). We provide a Lyapunov analysis for … Read more