Hilbertian convex feasibility problem: Convergence of projection methods

1997 ◽  
Vol 35 (3) ◽  
pp. 311-330 ◽  
Author(s):  
P. L. Combettes
Keyword(s):  
Projection Methods ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Convex Feasibility

CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT() SPACES

2018 ◽  
Vol 98 (1) ◽  
pp. 134-143 ◽  
Author(s):  
BYOUNG JIN CHOI
Keyword(s):  
Strong Convergence ◽  
Projection Method ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Alternating Projections ◽  
Normed Spaces ◽  
Closed Sets ◽  
Convex Feasibility ◽  
Alternating Projection ◽  
Iterative Projection Method

We study the convex feasibility problem in$\text{CAT}(\unicode[STIX]{x1D705})$spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$, and then we prove the$\unicode[STIX]{x1D6E5}$-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$.

Steered sequential projections for the inconsistent convex feasibility problem

2004 ◽  
Vol 59 (3) ◽  
pp. 385-405 ◽  
Author(s):  
Yair Censor ◽  
Alvaro R. De Pierro ◽  
Maroun Zaknoon
Keyword(s):  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Convex Feasibility
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