journal article Jan 01, 1993

On the convergence of von Neumann's alternating projection algorithm for two sets

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References
25
[1]
Bauschke, H. H. and Borwein, J. M.: Dykstra's alternating projection algorithm for two sets. Technical Report CORR 92-15, Faculty of Mathematics, University of Waterloo, May 1992, to appear inJ. Approx. Theory.
[2]
Borwein, J. M.: Convex relations in analysis and optimization, in S. Schaible and W. T. Ziemba, (eds),Generalized Concavity in Optimization and Economics, Academic Press, New York, pp. 335?377.
[3]
Borwein, J. M.: Stability and regular points of inequality systems. J. Optim. Theory Appl.48(1) (1986), 9?52. 10.1007/bf00938588
[4]
Borwein, J. M. and Lewis, A. S.: Partially finite convex programming Part I: Quasi relative interiors and duality theory,Math. Programming 57 (1992), 15?48. 10.1007/bf01581072
[5]
Borwein, J. M. and Lewis, A. S.: A Partially finite convex programming Part II: Explicit lattice models.Math. Programming 57 (1992), 49?83. 10.1007/bf01581073
[6]
Borwein, J. M. and Lewis, A. S.: A survey of convergence results for maximum entropy methods, Technical Report CORR 92-32, Faculty of Mathematics, University of Waterloo, September 1992.
[7]
Borwein, J. M., and Yost, D. T.: Absolute norms on vector lattices.Proc. Edinburgh Math. Soc.,27 (1984), 215?222. 10.1017/s0013091500022318
[8]
Censor, Y.: On variable block algebraic reconstruction techniques, in G. T. Herman, A. K. Louis, and F. Natterer (eds),Mathematical Methods in Tomography, Springer, New York, 1990, pp. 133?140.
[9]
Deutsch, F.: Rate of convergence of the method of alternating projections, in B. Brosowski and F. Deutsch (eds),Parametric Optimization and Approximation, Birkh�user, Basel, 1983, pp. 96?107.
[10]
Deutsch, F.: The method of alternating orthogonal projections, in S. P. Singh (ed),Approximation Theory, Spline Functions and Applications, Kluwer Academic Publ., Dordrecht, 1992, pp. 105?121. 10.1007/978-94-011-2634-2_5
[11]
Ekeland, I. and Temam, R.:Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976.
[12]
Franchetti, C. and Light, W.: On the von Neumann alternating algorithm in Hilbert space,J. Math. Anal. Appl. 114 (1986), 305?314. 10.1016/0022-247x(86)90085-5
[13]
Friedricks, K.: On certain inequalities and characteristic value problems for analytic functions and for functions of two variables,Trans. Amer. Math. Soc. 41 (1937), 321?364. 10.1090/s0002-9947-1937-1501907-0
[14]
Gubin, L. G., Polyak, B. T., and Raik, E. V.: The method of projections for finding the common point of convex sets,U.S.S.R. Comput. Math. and Math. Phys. 7 (6) (1967), 1?24. 10.1016/0041-5553(67)90113-9
[15]
Jameson, G. J. O.:Topology and Normed Spaces, Chapman and Hall, London, 1974.
[16]
Luenberger, D. G.:Optimization by Vector Space Methods, Wiley, New York, 1969.
[17]
Motzkin, T. S. and Schoenberg, I. J.: The relaxation method for linear inequalities,Canad. J. Math. 6 (1954), 393?404. 10.4153/cjm-1954-038-x
[18]
Pierra, G.: Decomposition through formalization in a product space,Math. Programming 28 (1984), 96?115. 10.1007/bf02612715
[19]
Robinson, S. M.: Regularity and stability for convex multivalued functions.Math. Oper. Res. 1 (2) (1976), 130?143. 10.1287/moor.1.2.130
[20]
Rockafellar, R. T.:Convex Analysis, Princeton University Press, Princeton, NJ, 1970. 10.1515/9781400873173
[21]
Rudin, W.:Functional Analysis, McGraw-Hill, New York, 1973.
[22]
Simoni?, A.: Personal communication.
[23]
Tijs, S. H. and Borwein, J. M.: Some generalizations of Carath�odory's theorem via barycenters, with application to mathematical programming,Canad. Math. Bull. 23 (3) (1980), 339?346. 10.4153/cmb-1980-048-x
[24]
Van Tiel, J.:Convex Analysis, Wiley, New York, 1984.
[25]
von Neumann, J.:Functional Operators, Vol. II, Princeton University Press, 1950. (Reprint of mimeographed lecture notes first distributed in 1933.)
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Published
Jan 01, 1993
Vol/Issue
1(2)
Pages
185-212
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H. H. Bauschke, J. M. Borwein (1993). On the convergence of von Neumann's alternating projection algorithm for two sets. Set-Valued Analysis, 1(2), 185-212. https://doi.org/10.1007/bf01027691