The Method of Alternating Relaxed Projections for Two Nonconvex Sets
Tóm tắt
Từ khóa
Tài liệu tham khảo
Aharoni, R., Censor, Y.: Block-iterative projection methods for parallel computation of solutions to convex feasibility problems. Linear Algebra Appl. 120, 165–175 (1989)
Baillon, J.B., Bruck, R.E., Reich, S.: On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces. Houst. J. Math. 4, 1–9 (1978)
Baillon, J.-B., Combettes, P.L., Cominetti, R.: Asymptotic behaviour of compositions of under-relaxed nonexpansive operators. arXiv:1304.7078 (2013)
Bauschke, H.H.: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J. Math. Anal. Appl. 202, 150–159 (1996)
Bauschke, H.H., Borwein, J.M.: On the convergence of von Neumann’s alternating projection algorithm for two sets. Set-Valued Anal. 1, 185–212 (1993)
Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367–426 (1996)
Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011)
Bauschke, H.H., Luke, D.R., Phan, H.M., Wang, X.: Restricted normal cones and the method of alternating projections: theory. Set-Valued Var. Anal. 21, 431–473 (2013)
Bauschke, H.H., Luke, D.R., Phan, H.M., Wang, X.: Restricted normal cones and the method of alternating projections: applications. Set-Valued Var. Anal. 21, 475–501 (2013)
Borwein, J.M., Vanderwerff, J.D.: Convex Functions. Cambridge University Press, Cambridge (2010)
Bruck, R.E., Reich, S.: Nonexpansive projections and resolvents of accretive operators in Banach spaces. Houst. J. Math. 3, 459–470 (1977)
Cegielski, A.: Iterative Methods for Fixed Point Problems in Hilbert Spaces. Lect. Notes Math., vol. 2057. Springer, Berlin (2012)
Censor, Y., Zenios, S.A.: Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, New York (1997)
Combettes, P.L.: Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization 53, 475–504 (2004)
Combettes, P.L., Trussell, H.J.: Method of successive projections for finding a common point of sets in metric spaces. J. Optim. Theory Appl. 67, 487–507 (1990)
Deutsch, F., Hundal, H.: The rate of convergence for the cyclic projections algorithm I: angles between convex sets. J. Approx. Theory 142, 36–55 (2006)
Deutsch, F., Hundal, H.: The rate of convergence for the cyclic projections algorithm II: norms of nonlinear operators. J. Approx. Theory 142, 56–82 (2006)
Deutsch, F., Hundal, H.: The rate of convergence for the cyclic projections algorithm III: regularity of convex sets. J. Approx. Theory 155, 155–184 (2008)
Goebel, K., Kirk, W.A.: Topics in Metric Fixed Point Theory. Cambridge University Press, Cambridge (1990)
Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Dekker, New York (1984)
Gubin, L.G., Polyak, B.T., Raik, E.V.: The method of projections for finding the common point of convex sets. USSR Comput. Math. Math. Phys. 7, 1–24 (1967)
Lewis, A.S., Luke, D.R., Malick, J.: Local linear convergence for alternating and averaged nonconvex projections. Found. Comput. Math. 9, 485–513 (2009)
Luke, D.R.: Finding best approximation pairs relative to a convex and prox-regular set in a Hilbert space. SIAM J. Optim. 19, 714–739 (2008)
Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis, corrected 3rd printing edn. Springer, Berlin (2009)
von Neumann, J.: Functional Operators, Vol. II: The Geometry of Orthogonal Spaces. Annals of Mathematical Studies, vol. 22. Princeton University Press, Princeton (1950)
Wang, X., Bauschke, H.H.: Compositions and averages of two resolvents: relative geometry of fixed point sets and a partial answer to a question by C. Byrne. Nonlinear Anal. 20, 131–153 (2012)