Inertial proximal incremental aggregated gradient method with linear convergence guarantees

Xiaoya Zhang, Wei Peng and Hui Zhang ()
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Xiaoya Zhang: Defense Innovation Institute, Chinese Academy of Military Science
Wei Peng: Defense Innovation Institute, Chinese Academy of Military Science
Hui Zhang: National University of Defense Technology

Mathematical Methods of Operations Research, 2022, vol. 96, issue 2, No 2, 187-213

Abstract: Abstract In this paper, we propose an inertial version of the Proximal Incremental Aggregated Gradient (abbreviated by iPIAG) method for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function. First, we prove that iPIAG converges linearly under the gradient Lipschitz continuity and the strong convexity, along with an upper bound estimation of the inertial parameter. Then, by employing the recent Lyapunov-function-based method, we derive a weaker linear convergence guarantee, which replaces the strong convexity by the quadratic growth condition. At last, we present two numerical tests to illustrate that iPIAG outperforms the original PIAG.

Keywords: Linear convergence; Inertial method; Quadratic growth condition; Incremental aggregated gradient; Lyapunov function; 90C30; 90C26; 47N10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00186-022-00790-0

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