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Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems.
S. Kaczmarz, Angenaherte Auflosung von Systemen linearer Gleichungen , Bull. Acad. Sci. Pologne, A35: 355–357, 1937
1937
Earlier work this paper cites.
J. von Neumann, Functional operators , Princeton University Press, 1950
1950
Earlier work this paper cites.
T. Motzkin and I. Schoenberg, The relaxation method for linear inequalities , Canad. J. Math., 6: 393–404, 1954
1954
Earlier work this paper cites.
L.G. Gubin, B.T. Polyak and E.V. Raik, The method of projections for finding the common point of convex sets , USSR Computational Mathematics and Mathematical Physics, 7(6): 1–24, 1967
1967
Earlier work this paper cites.
J.V. Burke and M.C. Ferris, Weak sharp minima in mathematical programming , SIAM Journal of Control and Optimization, 31(6): 1340–1359, 1993
1993
Earlier work this paper cites.
H.H. Bauschke and J.M. Borwein, On projection algorithms for solving convex feasibility problems , SIAM Review 38(3): 367–426, 1996
1996
Earlier work this paper cites.
P.L. Combettes, The convex feasibility problem in image recovery , Advances in Imaging and Electron Physics, 95, 155–270, 1996
1996
Earlier work this paper cites.
G. H. Golub and C. F. Van Loan, Matrix Computations , Johns Hopkins University Press; 3rd edition, 1996
1996
Earlier work this paper cites.
P.L. Combettes, Hilbertian convex feasibility problem: convergence of projection methods , Applied Mathematics & Optimization, 35: 311-330, 1997
1997
Earlier work this paper cites.
H. Stark and Y. Yang, Vector Space Projections : A Numerical Approach to Signal and Image Processing , Neural Nets and Optics, Wiley-Interscience, 1998
1998
Earlier work this paper cites.
G. Sharma, Set theoretic estimation for problems in subtractive color , Color Res. Appl., 25: 333–348, 2000
2000
Earlier work this paper cites.
A. Auslender, M. Teboulle, A Log-Quadratic Projection Method for Convex Feasibility Problems , Studies in Computational Mathematics, 8: 1–9, 2001
2001
Earlier work this paper cites.
C. Byrne and Y. Censor, Proximity function minimization using multiple Bregman projections, with applications to split feasibility and Kullback-Leibler distance minimization , Annals of Operations Research, 105(1): 77-98, 2001
2001
Earlier work this paper cites.
Y. Censor, T. Elfving and G.T. Herman, Averaging strings of sequential iterations for convex feasibility problems. In: D. Butnariu, Y. Censor and S. Reich (editors), Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Elsevier Science Publishers, 101–114, 2001
2001
Cited alongside, same era.
A. Beck and M. Teboulle, Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems , Optimization Methods and Software, 18(4): 377–394, 2003
2003
Cited alongside, same era.
A. Beck and M. Teboulle, A conditional gradient method with linear rate of convergence for solving convex linear systems , Mathematical Methods of Operations Research 59(2): 235–247, 2004
2004
Cited alongside, same era.
H. Choi, R.G. Baraniuk, Multiple wavelet basis image denoising using Besov ball projections , IEEE Signal Process. Lett. 11, 717 - 720, 2004
2004
Cited alongside, same era.
T. Strohmer and R. Vershynin, A randomized Kaczmarz algorithm with exponential convergence , Journal of Fourier Analysis and Applications, 15, 2009
2009
Later among the works it cites.
D. Leventhal and A. Lewis, Randomized methods for linear constraints: convergence rates and conditioning , Mathematics of Operations Research, 35(3): 641 - 654, 2010
2010
Later among the works it cites.
Y.M. Lu, M. Karzand and M. Vetterli, Demosaicking by alternating projections: Theory and fast one-step implementation , IEEE Trans. Image Process., 19(8): 2085–2098, 2010
2010
Later among the works it cites.
A. Nedic, Random Projection Algorithms for Convex Set Intersection Problems , 49th IEEE Conference on Decision and Control, 7655–7660, 2010
2010
Later among the works it cites.
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J. Gu, H. Stark and Y. Yang, Wide-band smart antenna design using vector space projection methods , IEEE Trans. Antennas Propag., 52: 3228–3236, 2004
2004
Cited alongside, same era.
A.A. Samsonov, E.G. Kholmovski, D.L. Parker, C.R. Johnson, POCSENSE: POCS- based reconstruction for sensitivity encoded magnetic resonance imaging , Magn. Reson. Med., 52: 139–1406, 2004
2004
Cited alongside, same era.
A. Liew, H. Yan and N. Law, POCS-based blocking artifacts suppression using a smoothness constraint set with explicit region modeling , IEEE Trans. Circuits Syst. Video Technol. 15: 795–800, 2005
2005
Cited alongside, same era.
D. Blatt and A.O.Hero, Energy based sensor network source localization via projection onto convex sets , IEEE Transactions on Signal Processing, 54(9): 3614–3619, 2006
2006
Cited alongside, same era.
F. Deutsch and H. Hundal, The rate of convergence for the cyclic projections algorithm I: Angles between convex sets , Journal of Approximation Theory, 142, 36-55, 2006
2006
Cited alongside, same era.
2006
Cited alongside, same era.
G.T. Herman, W. Chen, A fast algorithm for solving a linear feasibility problem with application to intensity-modulated radiation therapy , Linear Algebra Appl., 428, 1207–1217, 2008
2008
Cited alongside, same era.
G.T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections , Springer, New York, 2009
2009
Cited alongside, same era.
2011
Later among the works it cites.
H.H. Bauschke, P.L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces , Springer, New York, 2011
2011
Later among the works it cites.
A. Nedic, Random Algorithms for Convex Minimization Problems , Mathematical Programming, Series B, 129: 225–253, 2011
2011
Later among the works it cites.
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, 51(3): 1065–1088, 2012
2012
Later among the works it cites.
H.H. Bauschke, D. Noll, On cluster points of alternating projections , Serdica Mathematical Journal, 39: 355–364, 2013
2013
Later among the works it cites.
I. Necoara, Yu. Nesterov, F. Glineur, Linear convergence of first order methods for non-strongly convex optimization , submitted, 2015
2015
Later among the works it cites.
R. M. Gower and P. Richtarik, Randomized iterative methods for linear systems , SIAM Journal on Matrix Analysis and Applications, 36(4): 1660–1690, 2015
2015
Later among the works it cites.
A. Patrascu and I. Necoara, Nonasymptotic convergence of stochastic proximal point algorithms for constrained convex optimization , Journal of Machine Learning Research, 2017 (to appear)
2017
Later among the works it cites.