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arXiv · 1412.5563

Quantitative results on Fejer monotone sequences

Ulrick Kohlenbach·Laurentiu Leustean·Adriana Nicolae
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Abstract

We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These quantitative versions are in the form of explicit rates of so-called metastability in the sense of T. Tao. Our approach covers examples ranging from the proximal point algorithm for maximal monotone operators to various fixed point iterations (x_n) for firmly nonexpansive, asymptotically nonexpansive, strictly pseudo-contractive and other types of mappings. Many of the results hold in a general metric setting with some convexity structure added (so-called W-hyperbolic spaces). Sometimes uniform convexity is assumed still covering the important class of CAT(0)-spaces due to Gromov.

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Ulrick Kohlenbach, Laurentiu Leustean, Adriana Nicolae. 2014-12-17. Quantitative results on Fejer monotone sequences. https://arxiv.org/abs/1412.5563

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