scholarly journals k -center Clustering under Perturbation Resilience

2020 ◽  
Vol 16 (2) ◽  
pp. 1-39
Author(s):  
Maria-Florina Balcan ◽  
Nika Haghtalab ◽  
Colin White
Keyword(s):  
Perturbation Resilience

Perturbation Resilience

2020 ◽  
pp. 95-119
Author(s):  
Konstantin Makarychev ◽  
Yury Makarychev
Keyword(s):  
Perturbation Resilience

Perturbation resilience and superiorization methodology of averaged mappings

2017 ◽  
Vol 33 (4) ◽  
pp. 044007 ◽  
Author(s):  
Hongjin He ◽  
Hong-Kun Xu
Keyword(s):  
Perturbation Resilience ◽  
Averaged Mappings

Convergence to approximate solutions and perturbation resilience of iterative algorithms

2017 ◽  
Vol 33 (4) ◽  
pp. 044005 ◽  
Author(s):  
Simeon Reich ◽  
Alexander J Zaslavski
Keyword(s):  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Perturbation Resilience

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 A new convergence analysis and perturbation resilience of some accelerated proximal forward–backward algorithms with errors

2017 ◽  
Vol 33 (4) ◽  
pp. 044001 ◽  
Author(s):  
Daniel Reem ◽  
Alvaro De Pierro
Keyword(s):  
Convergence Analysis ◽  
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.

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