Abstract
It is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively. In this paper we study such a method and analyze its convergence properties. A main feature of the method is its capability to decompose the projection problem into several small ones. For some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation.
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References
C.W. Cryer, “The solution of a quadratic programming problem using systematic overrelaxation,”SIAM Journal on Control 22 (1971) 385–392.
U. Eckhardt, “Quadratic programming by successive overrelaxation,” Kernforschungsanlage Jülich, Technical Report No. Jül-1064-MA, 1974.
S.-P. Han and G. Lou, “A parallel algorithm for a class of convex programs,” to appear inSIAM Journal on Control and Optimization (Oct., 1986).
O.L. Mangasarian, “Solution of symmetric linear complementarity problem by iterative methods,”Journal of Optimization Theory and its Applications 22 (1977) 465–485.
J.J. Moré, “The Levenberg-Marquardt algorithm: Implementation and theory,” in: G.A. Watson, ed.,Proceedings of the 1978 Dundee Conference on Numerical Analysis, Lecture Notes in Mathematics 630 (Springer-Verlag, Berlin, 1978) pp. 105–116.
J.-J. Moreau, “Proximité et sous-gradient d'une fonctionelle,”Bulletin de la Societe Mathematique de France 93 (1965) 273–299.
R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, New Jersey, 1970).
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This material is based on work supported in part by the National Science Foundation under Grant DMS-8602419 and by the Center for Supercomputing Research and Development, University of Illinois.
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Han, SP. A successive projection method. Mathematical Programming 40, 1–14 (1988). https://doi.org/10.1007/BF01580719
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DOI: https://doi.org/10.1007/BF01580719