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Inexact proximal Newton methods for self-concordant functions

Author

Listed:
  • Jinchao Li

    (University of California, Los Angeles)

  • Martin S. Andersen

    (Technical University of Denmark)

  • Lieven Vandenberghe

    (University of California, Los Angeles)

Abstract

We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity pattern of the inverse covariance matrix are imposed. In the numerical experiments the proximal Newton steps are computed by an accelerated proximal gradient method, and multifrontal algorithms for positive definite matrices with chordal sparsity patterns are used to evaluate gradients and matrix-vector products with the Hessian of the smooth component of the objective.

Suggested Citation

  • Jinchao Li & Martin S. Andersen & Lieven Vandenberghe, 2017. "Inexact proximal Newton methods for self-concordant functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 19-41, February.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-016-0566-9
    DOI: 10.1007/s00186-016-0566-9
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    Citations

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    Cited by:

    1. Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2021. "Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 79(1), pages 127-154, May.
    2. Ching-pei Lee & Stephen J. Wright, 2019. "Inexact Successive quadratic approximation for regularized optimization," Computational Optimization and Applications, Springer, vol. 72(3), pages 641-674, April.
    3. Tianxiang Liu & Akiko Takeda, 2022. "An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems," Computational Optimization and Applications, Springer, vol. 82(1), pages 141-173, May.
    4. Tianxiao Sun & Ion Necoara & Quoc Tran-Dinh, 2020. "Composite convex optimization with global and local inexact oracles," Computational Optimization and Applications, Springer, vol. 76(1), pages 69-124, May.

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