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

Author

Listed:
  • Pourya Behmandpoor

    (KU Leuven)

  • Puya Latafat

    (KU Leuven)

  • Andreas Themelis

    (Kyushu University)

  • Marc Moonen

    (KU Leuven)

  • Panagiotis Patrinos

    (KU Leuven)

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.

Suggested Citation

  • Pourya Behmandpoor & Puya Latafat & Andreas Themelis & Marc Moonen & Panagiotis Patrinos, 2024. "SPIRAL: a superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization," Computational Optimization and Applications, Springer, vol. 88(1), pages 71-106, May.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:1:d:10.1007_s10589-023-00550-8
    DOI: 10.1007/s10589-023-00550-8
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