scholarly journals The magnitude of the minimal displacement vector for compositions and convex combinations of firmly nonexpansive mappings

2018 ◽  
Vol 12 (7) ◽  
pp. 1465-1474 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Walaa M. Moursi
Keyword(s):  
Displacement Vector ◽  
Nonexpansive Mappings ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Minimal Displacement Vector

Shrinking projection methods for firmly nonexpansive mappings

2009 ◽  
Vol 71 (12) ◽  
pp. e1626-e1632 ◽  
Author(s):  
Koji Aoyama ◽  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Shrinking Projection Methods

scholarly journals Quantitative analysis of a subgradient-type method for equilibrium problems

2021 ◽  
Author(s):  
Nicholas Pischke ◽  
Ulrich Kohlenbach
Keyword(s):  
Quantitative Analysis ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Metric Regularity ◽  
Rates Of Convergence ◽  
Type Method ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Fixed Point Sets

AbstractWe use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers.

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