Convergence results for stochastic convex feasibility problem using random Mann and simultaneous projection iterative algorithms in Hilbert space

2021 ◽  
pp. 1-15
Author(s):  
Akaninyene Udo Udom ◽  
Chijioke Joel Nweke
Keyword(s):  
Hilbert Space ◽  
Iterative Algorithms ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Convex Feasibility ◽  
Convergence Results ◽  
Stochastic Convex Feasibility Problem

scholarly journals Iterative algorithms with seminorm-induced oblique projections

2003 ◽  
Vol 2003 (7) ◽  
pp. 387-406 ◽  
Author(s):  
Yair Censor ◽  
Tommy Elfving
Keyword(s):  
Existence And Uniqueness ◽  
Convex Sets ◽  
Iterative Algorithms ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Proximity Function ◽  
Oblique Projections ◽  
Convex Feasibility ◽  
Definition Of ◽  
Inconsistent Case

A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility problem, employing seminorm-induced oblique projections, is constructed and its convergence for the consistent case is established. The fully simultaneous algorithm converges also in the inconsistent case to the minimum of a certain proximity function.

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

scholarly journals Solving a Split Feasibility Problem by the Strong Convergence of Two Projection Algorithms in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Yaé Ulrich Gaba
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Convex Feasibility ◽  
Split Feasibility

The goal of this manuscript is to establish strong convergence theorems for inertial shrinking projection and CQ algorithms to solve a split convex feasibility problem in real Hilbert spaces. Finally, numerical examples were obtained to discuss the performance and effectiveness of our algorithms and compare the proposed algorithms with the previous shrinking projection, hybrid projection, and inertial forward-backward methods.

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