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Parametric Proximal-Point Methods

Author

Listed:
  • N. Pavel

    (Ohio University)

  • I. Raykov

    (Ohio University)

Abstract

The main purpose of the present work is to introduce two parametric proximal-point type algorithms involving the gradient (or subdifferential) of a convex function. We take advantage of some properties of maximal monotone operators to prove monotonicity and convergence rate conditions. One example in Hilbert spaces and two numerical examples with program realizations are presented.

Suggested Citation

  • N. Pavel & I. Raykov, 2008. "Parametric Proximal-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 85-107, October.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9408-0
    DOI: 10.1007/s10957-008-9408-0
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    References listed on IDEAS

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    1. Daniel Ralph, 1994. "Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 352-389, May.
    2. S. De Marchi & I. Raykov, 2006. "Parametric Method for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 411-430, September.
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