Superiorization

Superiorization and Perturbation Resilience of Algorithms: A Bibliography

compiled and continuously updated by Yair Censor

This page (at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html) is a, chronologically ordered, bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms, compiled and continuously updated by Yair Censor. If you know of a related work in any form (preprint, reprint, journal publication, conference report, abstract or poster, book chapter, thesis, etc.) that should be included here kindly write to me on: yair@math.haifa.ac.il with full bibliographic details, a DOI if available, and a PDF copy of the work if possible. Copyright notice: Downloads are supplied for personal academic use only. A download is considered equivalent to a pre-print or re-print request. Use is granted consistent with fair-use of a pre-print or re-print. By downloading any of the following materials you are agreeing to these terms.

 

This page was initiated on March 7, 2015, and has been last updated on March 30, 2018.

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Trailer:

   We replace the text that appeared in this trailer in the previous versions of the page with a quotation of three paragraphs from the preface to the special issue: Y. Censor, G.T. Herman and M. Jiang (Guest Editors), "Superiorization: Theory and Applications", Special Issue of the journal Inverse Problems, Volume 33, Number 4, April 2017 [50] (all references refer to the bibliography below), followed by some additional notes.

   "The superiorization methodology is used for improving the efficacy of iterative algorithms whose convergence 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 iterative algorithm. The perturbed algorithm is called the 'superiorized version' of the original unperturbed algorithm. If the original algorithm is computationally efficient and useful in terms of the application at hand and if the perturbations are simple and not expensive to calculate, then the advantage of this method is that, for essentially the computational cost of the original algorithm, we are able to get something more desirable by steering its iterates according to the designed perturbations. This is a very general principle that has been used successfully in some important practical applications, especially for inverse problems such as image reconstruction from projections, intensity-modulated radiation therapy and nondestructive testing, and awaits to be implemented and tested in additional fields.

   An important case is when the original algorithm is 'feasibility-seeking' (in the sense that it strives to find some point that is compatible with a family of constraints) and the perturbations that are introduced into the original iterative algorithm aim at reducing (not necessarily minimizing) a given merit function. In this case superiorization has a unique place in optimization theory and practice. Many constrained optimization methods are based on methods for unconstrained optimization that are adapted to deal with constraints. Such is, for example, the class of projected gradient methods wherein the unconstrained minimization inner step 'leads' the process and a projection onto the whole constraint set (the feasible set) is performed after each minimization step in order to regain feasibility. This projection onto the constraints set is in itself a non-trivial optimization problem and the need to solve it in every iteration hinders projected gradient methods and limits their efficiency only to feasible sets that are 'simple to project onto.' Barrier or penalty methods likewise are based on unconstrained optimization combined with various 'add-on's that guarantee that the constraints are preserved. Regularization methods embed the constraints into a 'regularized' objecive function and proceed with unconstrained solution methods for the new regularized objective function.

   In contrast to these approaches, the superiorization methodology can be viewed as an antipodal way of thinking. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce merit function values. This is done while retaining the feasibility-seeking nature of the algorithm and without paying a high computational price. Furthermore, general-purpose approaches have been developed for automatically superiorizing iterative algorithms for large classes of constraints sets and merit functions; these provide algorithms for many application tasks." (end of qoute.)

   To a novice on the superiorization methodology and perturbation resilience of algorithms we recommend to read first the recent reviews in [16, 25, 39]. For a recent description of previous work that is related to superiorization but is not included here, such as the works of Sidky and Pan, e.g., [6], we direct the reader to [24, section 3]. The SNARK14 software package [42], with its in-built capability to superiorize iterative algorithms to improve their performance, can be helpful to practitioners. Naturally there is variability among the bibliography items below in their degree of relevance to the superiorization methodology and perturbation resilience of algorithms. In some, such as in, e.g., [23] below, superiorization does not appear in the title, abstract or introduction but only inside the work, e.g., [23, Subsection 6.2.1: Optimization vs. Superiorization].

   A word about the history. The terms and notions "superiorization" and "perturbation resilience" first appeared in the 2009 paper of Davidi, Herman and Censor [7] which followed its 2007 forerunner by Butnariu, Davidi, Herman and Kazantsev [3]. The ideas have some of their roots in the 2006 and 2008 papers of Butnariu, Reich and Zaslavski [2, 4]. All these culminated in Ran Davidi's 2010 Ph.D. dissertation [13].

The Bibliography:

[1]   P.L. Combettes, On the numerical robustness of the parallel projection method in signal synthesis, IEEE Signal Processing Letters, Vol. 8, pp. 45-47, (2001). DOI:10.1109/97.895371. [Abstract].

[2]   D. Butnariu, S. Reich and A.J. Zaslavski, Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces, in: H.F. Nathansky, B.G. de Buen, K. Goebel, W.A. Kirk, and B. Sims (Editors), Fixed Point Theory and its Applications, (Conference Proceedings, Guanajuato, Mexico, 2005), Yokahama Publishers, Yokahama, Japan, pp. 11-32, 2006. http://www.ybook.co.jp/pub/ISBN%20978-4-9465525-0.htm. [Abstract].

[3]   D. Butnariu, R. Davidi, G.T. Herman and I.G. Kazantsev, Stable convergence behavior under summable perturbations of a class of projection methods for convex feasibility and optimization problems, IEEE Journal of Selected Topics in Signal Processing, Vol. 1, pp. 540-547, (2007). DOI:10.1109/JSTSP.2007.910263. [Abstract].

[4]   D. Butnariu, S. Reich and A.J. Zaslavski, Stable convergence theorems for infinite products and powers of nonexpansive mappings, Numerical Functional Analysis and Optimization, Vol. 29, pp. 304-323, (2008). DOI:10.1080/01630560801998161. [Abstract].

[5]   G.T. Herman and R. Davidi, Image reconstruction from a small number of projections, Inverse Problems, Vol. 24, 045011 (17pp), (2008). DOI:10.1088/0266-5611/24/4/045011. [Abstract].

[6]   E.Y. Sidky and X. Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Physics in Medicine and Biology, Vol. 53,  pp. 4777-4807, (2008). DOI:10.1088/0031-9155/53/17/021. [Abstract].

[7]   R. Davidi, G.T. Herman and Y. Censor, Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections, International Transactions in Operational Research, Vol. 16, pp. 505-524, (2009). DOI:10.1111/j.1475-3995.2009.00695.x. Final version preprint PDF (624KB) file. E-reprint of published paper available upon request.

[8]   G.T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, Springer-Verlag, London, UK, 2nd Edition, 2009. DOI:10.1007/978-1-84628-723-7.

[9]   S.N. Penfold, Image Reconstruction and Monte Carlo Simulations in the Development of Proton Computed Tomography for Applications in Proton Radiation Therapy, Ph.D. dissertation, Centre for Medical Radiation Physics, University of Wollongong, 2010. http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4305&context=theses. [Abstract].

[10]   S.N. Penfold, R.W. Schulte, Y. Censor, V. Bashkirov, S. McAllister, K.E. Schubert and A.B. Rosenfeld, Block-iterative and string-averaging projection algorithms in proton computed tomography image reconstruction, in: Y. Censor, M. Jiang and G. Wang (Editors), Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Medical Physics Publishing, Madison, WI, USA, 2010, pp. 347-367. Final version preprint PDF (463KB) file. E-reprint of published paper available upon request. https://www.medicalphysics.org/SimpleCMS.php?content=reviewlist.php&isbn=9781930524484.

[11]   Y. Censor, R. Davidi and G.T. Herman, Perturbation resilience and superiorization of iterative algorithms, Inverse Problems, Vol. 26, (2010) 065008 (12pp). DOI:10.1088/0266-5611/26/6/065008. Final version preprint PDF (394KB) file. E-reprint of published paper available upon request.

[12]   S.N. Penfold, R.W. Schulte, Y. Censor and A.B. Rosenfeld, Total variation superiorization schemes in proton computed tomography image reconstruction, Medical Physics, Vol. 37, pp. 5887-5895, (2010). DOI:10.1118/1.3504603. Final version preprint PDF (339KB) file. E-reprint of published paper available upon request.

[13]   R. Davidi, Algorithms for Superiorization and their Applications to Image Reconstruction, Ph.D. dissertation, Department of Computer Science, The City University of New York, NY, USA, 2010. http://gradworks.umi.com/34/26/3426727.html. [Abstract].

[14]   E. Garduño, G.T. Herman and R. Davidi, Reconstruction from a few projections by ℓ1-minimization of the Haar transform, Inverse Problems, Vol. 27, 055006, (2011). DOI:10.1088/0266-5611/27/5/055006. [Abstract].

[15]   Y. Censor, W. Chen, P.L. Combettes, R. Davidi and G.T. Herman, On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Computational Optimization and Applications, Vol. 51, pp. 1065-1088, (2012). DOI:10.1007/s10589-011-9401-7. Final version preprint PDF (721KB) file. E-reprint of published paper available upon request. A related (unpublished) Technical Report: W. Chen, Data sets of very large linear feasibility problems solved by projection methods, March 2, 2011, can be viewed here: PDF (66KB).

[16]   G.T. Herman, E. Garduño, R. Davidi and Y. Censor, Superiorization: An optimization heuristic for medical physics, Medical Physics, Vol. 39, pp. 5532-5546, (2012). DOI:10.1118/1.4745566. Final version preprint PDF (1,193KB) file. E-reprint of published paper available upon request.

[17]   R. Davidi, R.W. Schulte, Y. Censor and L. Xing, Fast superiorization using a dual perturbation scheme for proton computed tomography, Transactions of the American Nuclear Society, Vol. 106, pp. 73-76, (2012). Final version preprint PDF (591KB) file. E-reprint of published paper available upon request.

[18]   T. Nikazad, R. Davidi and G.T. Herman, Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction, Inverse Problems, Vol. 28, 035005 (19pp), (2012). DOI:10.1088/0266-5611/28/3/035005. [Abstract].

[19]   D. Steinberg, V. Bashkirov, V. Feng, R.F. Hurley, R.P. Johnson, S. Macafee, T. Plautz, H.F.-W. Sadrozinski, R. Schulte and A. Zatserklyaniy, Monte Carlo simulations for the development a clinical proton CT scanner, Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), 2012 IEEE, pp. 1311-1315. Oct. 27-Nov. 3, 2012, Anaheim, CA, USA. DOI:10.1109/NSSMIC.2012.6551320. [Abstract].

[20]   W. Jin, Y. Censor and M. Jiang, A heuristic superiorization-like approach to bioluminescence, International Federation for Medical and Biological Engineering (IFMBE) Proceedings, Vol. 39, pp. 1026-1029, (2013). DOI:10.1007/978-3-642-29305-4_269. Final version preprint PDF (297KB) file. E-reprint of published paper available upon request.

[21]   Y. Censor and A.J. Zaslavski, Convergence and perturbation resilience of dynamic string-averaging projection methods, Computational Optimization and Applications, Vol. 54, pp. 65-76, (2013). DOI:10.1007/s10589-012-9491-x. Final version preprint PDF (209KB) file. E-reprint of published paper available upon request.

[22]   S.-S. Luo, Reconstruction Algorithms for Single-photon Emission Computed Tomography, Ph.D. dissertation, Computational Mathematics, Peking University (PKU), Beijing, P.R. China, 2013. http://www.dissertationtopic.net/doc/2220625. [Abstract].

[23]   X. Zhang, Prior-Knowledge-Based Optimization Approaches for CT Metal Artifact Reduction, Ph.D. dissertation, Dept. of Electrical Engineering, Stanford University, Stanford, CA, USA, 2013. http://purl.stanford.edu/ws303zb5770. [Abstract].

[24]   Y. Censor, R. Davidi, G.T. Herman, R.W. Schulte and L. Tetruashvili, Projected subgradient minimization versus superiorization, Journal of Optimization Theory and Applications, Vol. 160, pp. 730-747, (2014). DOI:10.1007/s10957-013-0408-3. Final version preprint PDF (480KB) file. E-reprint of published paper available upon request.

[25]   G.T. Herman, Superiorization for image analysis, in: Combinatorial Image Analysis, Lecture Notes in Computer Science Vol. 8466, Springer, 2014, pp. 1-7. DOI:10.1007/978-3-319-07148-0_1. [Abstract].

[26]   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). DOI:10.3934/ipi.2014.8.223. [Abstract].

[27]   M.J. Schrapp and G.T. Herman, Data fusion in X-ray computed tomography using a superiorization approach, Review of Scientific Instruments, Vol. 85, 053701 (9pp), (2014). DOI:10.1063/1.4872378. [Abstract].

[28]   M. Schrapp, M. Goldammer, K. Schörner and J. Stephan, Improvement of image quality in computed tomography via data fusion, Proceedings of the 5th International Conference on Industrial Computed Tomography (iCT), pp. 283-289, February 2014, the University of Applied Sciences, Wels, Upper Austria. http://www.ndt.net/article/ctc2014/papers/283.pdf. [Abstract].

[29]   E. Garduño and G.T. Herman, Superiorization of the ML-EM algorithm, IEEE Transactions on Nuclear Science, Vol. 61, pp. 162-172, (2014). DOI:10.1109/TNS.2013.2283529. [Abstract].

[30]   O. Langthaler, Incorporation of the Superiorization Methodology into Biomedical Imaging Software, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, September 2014, (76 pages). http://www.marshallplan.at/images/papers_ scholarship/2014/Salzburg_University_of_Applied_Sciences_LangthalerOliver_2014.pdf. [Abstract].

[31]   B. Prommegger, Verification and Evaluation of Superiorized Algorithms Used in Biomedical Imaging: Comparison of Iterative Algorithms With and Without Superiorization for Image Reconstruction from Projections, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, October 2014, (84 pages). http://www.marshallplan.at/images/papers_ scholarship/2014/Salzburg_University_of_Applied_Sciences_PrommeggerBernhard_2014.pdf. [Abstract].

[32]   D.C. Hansen, Improving Ion Computed Tomography, Ph.D. dissertation, Aarhus University, Experimental Clinical Oncology, Aarhus, Denmark, 2014. http://pure.au.dk//portal/files/83515131/dissertation.pdf. [Abstract].

[33]   J. Lee, C. Kim, B. Min, J. Kwak, S. Park, S-B. Lee, S. Park and S. Cho, Sparse-view proton computed tomography using modulated proton beams, Medical Physics, Vol. 42, pp. 1129-1137, (2015). DOI:10.1118/1.4906133. [Abstract].

[34]   T. Nikazad and M. Abbasi, Perturbation-resilient iterative methods with an infinite pool of mappings, SIAM Journal on Numerical Analysis, Vol. 53, pp. 390-404, (2015). DOI:10.1137/14095724X. [Abstract].

[35]   F. Arroyo, E. Arroyo, X. Li and J. Zhu, The convergence of the block cyclic projection with an overrelaxation parameter for compressed sensing based tomography, Journal of Computational and Applied Mathematics, Vol. 280, pp. 59-67, (2015). DOI:10.1016/j.cam.2014.11.036. [Abstract].

[36]   R. Davidi, Y. Censor, R.W. Schulte, S. Geneser and L. Xing, Feasibility-seeking and superiorization algorithms applied to inverse treatment planning in radiation therapy, Contemporary Mathematics, Vol. 636, pp. 83-92, (2015). DOI:10.1090/conm/636/12729. Final version preprint PDF (454KB) file. E-reprint of published paper available upon request.

[37]   Y. Censor and D. Reem, Zero-convex functions, perturbation resilience, and subgradient projections for feasibility-seeking methods, Mathematical Programming, Series A, Vol. 152, pp. 339-380, (2015). DOI:10.1007/s10107-014-0788-7. Final version preprint PDF (589KB) file. E-reprint of published paper available upon request.

[38]   Y. Censor and A.J. Zaslavski, Strict Fejér monotonicity by superiorization of feasibility-seeking projection methods, Journal of Optimization Theory and Applications, Vol. 165, pp. 172-187, (2015). DOI:10.1007/s10957-014-0591-x. Final version preprint PDF (216KB) file. E-reprint of published paper available upon request.

[39]   Y. Censor, Weak and strong superiorization: Between feasibility-seeking and minimization, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, Vol. 23, pp. 41-54, (2015). DOI:10.1515/auom-2015-0046. Final version preprint PDF (213KB) file. E-reprint of published paper available upon request.

[40]   H.H. Bauschke and V.R. Koch, Projection methods: Swiss army knives for solving feasibility and best approximation problems with half-spaces, Contemporary Mathematics, Vol. 636, pp. 1-40, (2015). DOI:10.1090/conm/636/12726. https://people.ok.ubc.ca/bauschke/Research/c16.pdf. [Abstract].

[41]   M.J. Schrapp, Multi Modal Data Fusion in Industrial X-ray Computed Tomography, Ph.D. dissertation, Fakultät für Physik der Technischen Universität München, Munich, Germany, 2015. [Abstract].

[42]   SNARK14, A programming system for the reconstruction of 2D images from 1D projections designed to help researchers in developing and evaluating reconstruction algorithms. In particular, SNARK14 can be used for automatic superiorization of any iterative reconstruction algorithm. Released: 2015. Go to SNARK14.

[43]   W. Jin, Y. Censor and M. Jiang, Bounded perturbation resilience of projected scaled gradient methods, Computational Optimization and Applications, Vol. 63, pp. 365-392, (2016). DOI:10.1007/s10589-015-9777-x. Final version preprint PDF (357KB) file. E-reprint of published paper available upon request.

[44]   Q-L. Dong, J. Zhao and S. He, Bounded perturbation resilience of the viscosity algorithm, Journal of Inequalities and Applications, 2016:299 (12pp), 2016. DOI:10.1186/s13660-016-1242-6. [Abstract].

[45]   E. Nurminski, Finite-value superiorization for variational inequality problems, arXiv:1611.09697, (2016). [arXiv:1611.09697]. [Abstract].

[46]   S. Luo, Y. Zhang, T. Zhou and J. Song, Superiorized iteration based on proximal point method and its application to XCT image reconstruction, arXiv:1608.03931, (2016). [arXiv:1608.03931]. [Abstract].

[47]   Y. Censor and Y. Zur, Linear superiorization for infeasible linear programming, in: Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski and P. Pardalos (Editors), Discrete Optimization and Operations Research, Lecture Notes in Computer Science (LNCS), Vol. 9869, (2016), Springer International Publishing, pp. 15-24. DOI:10.1007/978-3-319-44914-2_2. [Abstract]. Reprint of the paper is available for free download on the publisher's website, under the link: "Download Sample pages 2 PDF (774.4 KB)" thereon.

[48]   C. Havas, Revised Implementation and Empirical Study of Maximum Likelihood Expectation Maximization Algorithms with and without Superiorization in Image Reconstruction, Marshall Plan Scholarship Report, Salzburg University of Applied Sciences, Salzburg, Austria, and The Graduate Center of the City University of New York, NY, USA, October 2016, (49 pages). https://static1.squarespace.com/static/559921a3e4b02c1d7480f8f4/t/596c97aad1758e1c6808c0fa/1500288944245/ Havas+Clemens_615.pdf. [Front Matter].

[49]   T. Humphries, J. Winn and A. Faridani, Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data, Physics in Medicine and Biology, Vol. 62 (2017), 6762. https://doi.org/10.1088/1361-6560/aa7c2d. [Abstract].

[50]   Y. Censor, G.T. Herman and M. Jiang, Guest Editors, Superiorization: Theory and Applications, Special Issue of the journal Inverse Problems, Volume 33, Number 4, April 2017. Read the Preface to the special issue on the journal's website, or here Preface. Read the titles and abstracts of all 14 papers included in the special issue on the journal's website at: titles and abstracts or consult items [51]-[64] below.

[51]   D. Reem and A. De Pierro, A new convergence analysis and perturbation resilience of some accelerated proximal forward-backward algorithms with errors, Inverse Problems, Vol. 33 (2017), 044001. https://doi.org/10.1088/1361-6420/33/4/044001. [Abstract].

[52]   T. Nikazad and M. Abbasi, A unified treatment of some perturbed fixed point iterative methods with an infinite pool of operators, Inverse Problems, Vol. 33 (2017), 044002. https://doi.org/10.1088/1361-6420/33/4/044002. [Abstract].

[53]    M. Yamagishi and I. Yamada, Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization, Inverse Problems, Vol. 33 (2017), 044003. https://doi.org/10.1088/1361-6420/33/4/044003. [Abstract].

[54]    A.J. Zaslavski, Asymptotic behavior of two algorithms for solving common fixed point problems, Inverse Problems, Vol. 33 (2017), 044004. https://doi.org/10.1088/1361-6420/33/4/044004. [Abstract].

[55]   S. Reich and A.J. Zaslavski, Convergence to approximate solutions and perturbation resilience of iterative algorithms, Inverse Problems, Vol. 33 (2017), 044005. https://doi.org/10.1088/1361-6420/33/4/044005. [Abstract].

[56]   Y. Censor, Can linear superiorization be useful for linear optimization problems? Inverse Problems, Vol. 33 (2017), 044006 (22pp). https://doi.org/10.1088/1361-6420/33/4/044006. [Abstract]. E-reprint of published paper available upon request.

[57]   H. He and H-K. Xu, Perturbation resilience and superiorization methodology of averaged mappings, Inverse Problems, Vol. 33 (2017), 044007. https://doi.org/10.1088/1361-6420/33/4/044007. [Abstract].

[58]   H-K. Xu, Bounded perturbation resilience and superiorization techniques for the projected scaled gradient method, Inverse Problems, Vol. 33 (2017), 044008. https://doi.org/10.1088/1361-6420/33/4/044008. [Abstract].

[59]   A. Cegielski and F. Al-Musallam, Superiorization with level control, Inverse Problems, Vol. 33 (2017), 044009. https://doi.org/10.1088/1361-6420/aa5d79. [Abstract].

[60]   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. https://doi.org/10.1088/1361-6420/33/4/044010. [Abstract].

[61]   E. Garduño and G.T. Herman, Computerized tomography with total variation and with shearlets, Inverse Problems, Vol. 33 (2017), 044011. https://doi.org/10.1088/1361-6420/33/4/044011. [Abstract].

[62]   E. Bonacker, A. Gibali, K-H. Küfer and P. Süss, Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy treatment, Inverse Problems, Vol. 33 (2017), 044012. https://doi.org/10.1088/1361-6420/33/4/044012. [Abstract].

[63]   J. Zhu and S. Penfold, Total variation superiorization in dual-energy CT reconstruction for proton therapy treatment planning, Inverse Problems, Vol. 33 (2017), 044013. https://doi.org/10.1088/1361-6420/33/4/044013. [Abstract].

[64]   Q. Yang, W. Cong and G. Wang, Superiorization-based multi-energy CT image reconstruction, Inverse Problems, Vol. 33 (2017), 044014. https://doi.org/10.1088/1361-6420/aa5e0a. [Abstract].

[65]   T. Nikazad, M. Abbasi and T. Elfving, Error minimizing relaxation strategies in Landweber and Kaczmarz type iterations, Journal of Inverse and Ill-posed Problems, Vol. 25, pp. 35-56, (2017). DOI:10.1515/jiip-2015-0082. [Abstract].

[66]   Q.L. Dong, Y.J. Cho and Th.M. Rassias, Multi-step inertial Krasnosel'ski-Mann algorithm for nonexpansive operators, [Preprint from ResearchGate] (2017).

[67]   C.O.S. Sorzano, J. Vargas, J. Otón, J.M. de la Rosa-Trevín, J.L. Vilas, M. Kazemi, R. Melero, L. del Caño, J. Cuenca, P. Conesa, J. Gómez-Blanco, R. Marabini and J.M. Carazo, A survey of the use of iterative reconstruction algorithms in electron microscopy, BioMed Research International, Vol. 2017 (2017), Article ID 6482567, 17 pages, https://doi.org/10.1155/2017/6482567. [Free download of full paper from the publisher at hindawi.com]. Also [here, 1,413KB].

[68]   C.L. Byrne, The Dykstra and Bregman-Dykstra algorithms as superiorization (December 26, 2017). Technical report, (2017). [Preprint from ResearchGate].

[69]   Q.-L. Dong, A. Gibali, D. Jiang and S.-H. Ke, Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery, Fixed Point Theory and Applications, accepted for publication, (2017). [Preprint from arXiv].

[70]   Q.-L. Dong, A. Gibali, D. Jiang and Y.-C. Tang, Bounded perturbation resilience of extragradient-type methods and their applications, Journal of Inequalities and Applications, (2017) 2017:280. DOI:10.1186/s13660-017-1555-0. [Free download of full paper from the publisher].

[71]   A. Gibali and S. Petra, DC-programming versus ℓ0-superiorization for discrete tomography, Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, accepted for publication, (2017). [Preprint from ResearchGate].

[72]   Yanni Guo, W. Cui and Yansha Guo, Perturbation resilience of proximal gradient algorithm for composite objectives, Journal of Nonlinear Sciences and Applications (JNSA), Vol. 10, pp. 5566-5575, (2017), http://dx.doi.org/10.22436/jnsa.010.10.36. [Free download of full paper from the publisher at http://www.isr-publications.com/jnsa]. Also [here, 693KB].

[73]   C. Bargetz, S. Reich and R. Zalas, Convergence properties of dynamic string averaging projection methods in the presence of perturbations, Numerical Algorithms, Vol. 77, pp. 185-209, (2018). https://doi.org/10.1007/s11075-017-0310-4. [Abstract].

[74]   M.V.W. Zibetti, C. Lin and G.T. Herman, Total variation superiorized conjugate gradient method for image reconstruction, Inverse Problems, Vol. 34 (2018), 034001. https://doi.org/10.1088/1361-6420/aaa49b. [Preprint from arXiv].

[75]   A. Gibali, K-H. Küfer, D. Reem and P. Süss, A generalized projection-based scheme for solving convex constrained optimization problems, Computational Optimization and Applications, accepted for publication (2018). [Preprint from ResearchGate].

[76]   B. Schultze, Y. Censor, P. Karbasi, K.E. Schubert, and R.W. Schulte, An improved method of total variation superiorization applied to reconstruction in proton computed tomography, Technical Report, March 3, 2018. (2018). Preprint PDF (3,015KB) file. Available on arXiv at: https://arxiv.org/abs/1803.01112.

[77]   Y. Censor, H. Heaton, and R.W. Schulte, Derivative-free superiorization with component-wise perturbations. Numerical Algorithms, accepted for publication. DOI:10.1007/s11075-018-0524-0. Preprint PDF (695KB) file. Available on arXiv at: https://arxiv.org/abs/1804.00123. Reprint available on: Springer Nature SharedIt.

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The Digital Object Identifier (DOI®) System is for identifying content objects in the digital environment. DOI names are assigned to any entity for use on digital networks. Simply google the whole string (e.g., DOI:10.1007/s11228-011-0192-x) in your browser to find locations of the object.