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Strong convergence of a proximal-based method for convex optimization

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Abstract.

In this work we study a proximal-like method for the problem of convex minimization in Hilbert spaces. Using the classical proximal mapping, we construct a new stable iterative procedure. The strong convergence of obtained sequences to the normal solution of the optimization problem is proved. Some results of this paper are extended for uniformly convex Banach spaces.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Sciences, EMA University of Greifswald, Jahnstr. 15a, D-17487 Greifswald, Germany (e-mail: azmjakov@uni-greifswald.de; e-mail: wschmidt@uni-greifswald.de), , , , , , DE

    Vadim Azhmyakov & Werner H. Schmidt

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  1. Vadim Azhmyakov
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  2. Werner H. Schmidt
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Manuscript received: May 2002/Final version received: November 2002

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Azhmyakov, V., Schmidt, W. Strong convergence of a proximal-based method for convex optimization. Mathematical Methods of OR 57, 393–407 (2003). https://doi.org/10.1007/s001860200261

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  • DOI: https://doi.org/10.1007/s001860200261

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