Jaewook J. Suh – Optimization Online

Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms

Published: 2026/09/30

This paper presents Peppy, an AI-assisted workflow for discovering tight, analytic convergence proofs for first-order optimization algorithms. Generic approaches to using LLMs to conduct mathematical research target an unspecified, broad spectrum of problems and sometimes use the Lean 4 proof assistant for formalization. On the other hand, Peppy leverages domain-specific knowledge more heavily and is … Read more

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

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