Finite Termination of a Generalized Perceptron Algorithm
Optimization and Control
2026-04-27 v1
Abstract
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several natural step sizes. We also examine what can go wrong without strict feasibility: finite convergence may fail even for one function, and with several functions the method may converge to a point outside the feasible set. The linear setting recovers the classical perceptron algorithm.
Cite
@article{arxiv.2604.22265,
title = {Finite Termination of a Generalized Perceptron Algorithm},
author = {Heinz H. Bauschke and Tran Thanh Tung},
journal= {arXiv preprint arXiv:2604.22265},
year = {2026}
}