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

Pourya Behmandpoor (), Puya Latafat, Andreas Themelis, Marc Moonen and Panagiotis Patrinos
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Pourya Behmandpoor: KU Leuven
Puya Latafat: KU Leuven
Andreas Themelis: Kyushu University
Marc Moonen: KU Leuven
Panagiotis Patrinos: KU Leuven

Computational Optimization and Applications, 2024, vol. 88, issue 1, No 3, 106 pages

Abstract: 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.

Keywords: Finite sum minimization; Nonsmooth nonconvex optimization; Relative smoothness; Superlinear convergence; KL inequality; 90C06; 90C25; 90C26; 49J52; 49J53; 90C53 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00550-8

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