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math.OC2026
A Control-Theoretic Perspective on Optimal High-Order Optimization
Tianyi Lin, Michael. I. Jordan
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $Φ: \mathbb{R}^d…
math.OC2025
First-order methods almost always avoid saddle points: the case of vanishing step-sizes
Ioannis Panageas, Georgios Piliouras, Xiao Wang
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some of the most commonly used first order methods almost surely (under random initializations) and with ste…