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An inexact proximal regularization method for unconstrained optimization

Author

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  • Paul Armand

    (XLIM Laboratory – University of Limoges)

  • Isaï Lankoandé

    (XLIM Laboratory – University of Limoges)

Abstract

We present a regularization algorithm to solve a smooth unconstrained minimization problem.This algorithm is suitable to solve a degenerate problem, when the Hessian is singular at a local optimal solution. The main feature of our algorithm is that it uses an outer/inner iteration scheme. We show that the algorithm has a strong global convergence property under mild assumptions. A local convergence analysis shows that the algorithm is superlinearly convergent under a local error bound condition. Some numerical experiments are reported.

Suggested Citation

  • Paul Armand & Isaï Lankoandé, 2017. "An inexact proximal regularization method for unconstrained optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 43-59, February.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-016-0561-1
    DOI: 10.1007/s00186-016-0561-1
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    References listed on IDEAS

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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. Marc Fuentes & Jérôme Malick & Claude Lemaréchal, 2012. "Descentwise inexact proximal algorithms for smooth optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 755-769, December.
    3. Hande Benson & David Shanno, 2014. "Interior-point methods for nonconvex nonlinear programming: cubic regularization," Computational Optimization and Applications, Springer, vol. 58(2), pages 323-346, June.
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    5. Paul Armand & Joël Benoist & Riadh Omheni & Vincent Pateloup, 2014. "Study of a primal-dual algorithm for equality constrained minimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 405-433, December.
    6. Ying-Jie Li & Dong-Hui Li, 2009. "Truncated regularized Newton method for convex minimizations," Computational Optimization and Applications, Springer, vol. 43(1), pages 119-131, May.
    7. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    8. Kenji Ueda & Nobuo Yamashita, 2014. "A regularized Newton method without line search for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 59(1), pages 321-351, October.
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    Cited by:

    1. Paul Armand & Ngoc Nguyen Tran, 2021. "Local Convergence Analysis of a Primal–Dual Method for Bound-Constrained Optimization Without SOSC," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 96-116, April.

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