An Analytic Center Self-Concordant Cut Method for the Convex Feasibility Problem

2001 ◽  
pp. 395-407
Author(s):  
Faranak Sharifi Mokhtarian ◽  
Jean-Louis Goffin
Keyword(s):  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Analytic Center ◽  
Convex Feasibility ◽  
Cut Method

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$\unicode[STIX]{x1D705}\geq 0$.

An analytic center quadratic cut method for the convex quadratic feasibility problem

2002 ◽  
Vol 93 (2) ◽  
pp. 305-325 ◽  
Author(s):  
Faranak Sharifi Mokhtarian ◽  
Jean-Louis Goffin
Keyword(s):  
Feasibility Problem ◽  
Analytic Center ◽  
Cut Method

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.

scholarly journals Stability of a convex feasibility problem

2019 ◽  
Vol 75 (4) ◽  
pp. 1061-1077
Author(s):  
Carlo Alberto De Bernardi ◽  
Enrico Miglierina ◽  
Elena Molho
Keyword(s):  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Convex Feasibility
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