English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we introduce the concept of modulus of regularity as a tool toanalyze the speed of convergence, including the finite termination, for classesof Fej\'er monotone sequences which appear in fixed point theory, monotoneoperator theory, and convex optimization. This concept allows for a unifiedapproach to several notions such as weak sharp minima, error bounds, metricsubregularity, H\"older regularity, etc., as well as to obtain rates ofconvergence for Picard iterates, the Mann algorithm, the proximal pointalgorithm and the cyclic algorithm. As a byproduct we obtain a quantitativeversion of the well-known fact that for a convex lower semi-continuous functionthe set of minimizers coincides with the set of zeros of its subdifferentialand the set of fixed points of its resolvent.

Moduli of regularity and rates of convergence for Fej\'er monotone sequences