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arXiv · 2207.08195

SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization

Pourya Behmandpoor·Puya Latafat·Andreas Themelis·Marc Moonen·Panagiotis Patrinos
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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.

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Pourya Behmandpoor, Puya Latafat, Andreas Themelis, Marc Moonen, Panagiotis Patrinos. 2022-07-17. SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization. https://doi.org/10.1007/s10589-023-00550-8

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