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posted Mar 12, 2019, 4:49 AM by Yaseen Raouf Mohammed   [ updated Apr 7, 2019, 5:40 AM ]
 SUPERIORIZATION AND ITS IMPORTANCE IN THE OPTIMIZATION

 Mohsen Hoseini


 Department of Mathematics,University of Kurdistan,Sanandaj,Kurdistan,Iran

  
 Abstract.
Superiorization is an iterative method for constrained optimiza- tion. It is used for improving the efficacy of an iterative method whose con- vergence is resilient to certain kinds of perturbations. Such perturbations are designed to force the perturbed algorithm to produce more useful results for the intended application than the ones that are produced by the original itera- tive algorithm. The perturbed algorithm is called the superiorized version of the original unperturbed algorithm. Superiorization is a great way in iterative algorithms to improve the convergence rate and control the input noise of the algorithm process.


 Keywords:
Nonexpansive mapping; Minimization over fixed point; Bounded perturbation resilience;
Superiorization.


 REFERENCES
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[3] E.S. Helou, M.V.W. Zibetti and E.X. Miqueles, Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction, Inverse Problems, Vol. 33 (2017), 044010.
[4] Q. Yang, W. Cong and G. Wang, Superiorization-based multi-energy CT image reconstruction, Inverse Problems, Vol. 33 (2017), 044014.
[5] S. Luo and T. Zhou, Superiorization of EM algorithm and its application in single-photon emission computed tomography (SPECT), Inverse Problems and Imaging, Vol. 8, pp. 223-246, (2014).
[6] R. Davidi, Y. Censor, R.W. Schulte, S. Geneser and L. Xing, Feasibilityseeking and superiorization algorithms applied to inverse treatment planning inradiationtherapy,ContemporaryMathematics, Vol.636,pp.83-92,(2015).
[7] E. Bonacker, A. Gibali, K-H. Kfer and P. Sss, Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment, Inverse Problems, Vol. 33 (2017).
[8] Superiorization: Theory and Applications, Special Issue of the journal Inverse Problems, Volume 33, Number 4, April 2017.
[9] H. He, H. Xu, Perturbation resilience and superiorization methodology of averaged mappings, Inverse Problems 33 (2017), 044007.

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