Solving a General Split Equality Problem Without Prior Knowledge of Operator Norms in Banach Spaces

2020 ◽  
Vol 76 (1) ◽  
Author(s):  
Gholamreza Zamani Eskandani ◽  
Masoumeh Raeisi
Keyword(s):  
Prior Knowledge ◽  
Banach Spaces ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Operator Norms

Solving the split equality problem without prior knowledge of operator norms

Optimization ◽  
2014 ◽  
Vol 64 (9) ◽  
pp. 1887-1906 ◽  
Author(s):  
Qiao-Li Dong ◽  
Songnian He ◽  
Jing Zhao
Keyword(s):  
Prior Knowledge ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Operator Norms

scholarly journals Split equality variational inequality problems for pseudomonotone mappings in Banach spaces

2021 ◽  
Vol 66 (1) ◽  
pp. 139-158
Author(s):  
Oganeditse A. Boikanyo ◽  
Habtu Zegeye
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Prior Knowledge ◽  
Banach Spaces ◽  
Lipschitz Continuity ◽  
Linear Operators ◽  
Variational Inequality Problems ◽  
Bounded Linear ◽  
Pseudomonotone Mappings ◽  
Operator Norms

"A new algorithm for approximating solutions of the split equality variational inequality problems (SEVIP) for pseudomonotone mappings in the setting of Banach spaces is introduced. Strong convergence of the sequence generated by the proposed algorithm to a solution of the SEVIP is then derived without assuming the Lipschitz continuity of the underlying mappings and without prior knowledge of operator norms of the bounded linear operators involved. In addition, we provide several applications of our method and provide a numerical example to illustrate the convergence of the proposed algorithm. Our results improve, consolidate and complement several results reported in the literature."

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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