SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization
Optimization and Control
2024-04-30 v2 Machine Learning
Abstract
We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art.
Cite
@article{arxiv.2207.08195,
title = {SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization},
author = {Pourya Behmandpoor and Puya Latafat and Andreas Themelis and Marc Moonen and Panagiotis Patrinos},
journal= {arXiv preprint arXiv:2207.08195},
year = {2024}
}