first order optimization

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

Categories Convex Optimization Tags , , ,

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

Near-optimal closed-loop method via Lyapunov damping for convex optimization

Categories Convex Optimization, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , ,

We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are only achieved by non-autonomous methods via open-loop damping (e.g., Nesterov’s algorithm), we show that our system is the first one featuring a closed-loop damping while exhibiting a rate arbitrarily close to the optimal one. … Read more

Projection free methods on product domains

Categories Convex Optimization, Nonlinear Optimization Tags , ,

Projection-free block-coordinate methods avoid high computational cost per iteration and at the same time exploit the particular problem structure of product domains. Frank-Wolfe-like approaches rank among the most popular ones of this type. However, as observed in the literature, there was a gap between the classical Frank-Wolfe theory and the block-coordinate case. Moreover, most of … Read more