Bounded perturbation resilience and superiorization techniques for the projected scaled gradient method

2017 ◽  
Vol 33 (4) ◽  
pp. 044008 ◽  
Author(s):  
Hong-Kun Xu
Keyword(s):  
Gradient Method ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience

scholarly journals Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 535
Author(s):  
Yanni Guo ◽  
Xiaozhi Zhao
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Real Hilbert Space ◽  
Gradient Algorithm ◽  
Original Algorithm ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience

In this paper, a multi-parameter proximal scaled gradient algorithm with outer perturbations is presented in real Hilbert space. The strong convergence of the generated sequence is proved. The bounded perturbation resilience and the superiorized version of the original algorithm are also discussed. The validity and the comparison with the use or not of superiorization of the proposed algorithms were illustrated by solving the l 1 − l 2 problem.

scholarly journals Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 197
Author(s):  
Yingying Li ◽  
Yaxuan Zhang
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Lasso Problem ◽  
Bounded Perturbations ◽  
Split Feasibility

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

scholarly journals Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 14 ◽  
Author(s):  
Peichao Duan ◽  
Xubang Zheng ◽  
Jing Zhao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Bounded Perturbation ◽  
Common Fixed Point Problem ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Split Common Fixed Point

In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.

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