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On Projection Algorithms for Solving Convex Feasibility Problems

Bauschke, Heinz H. and Borwein, Jonathan M. (1996) On Projection Algorithms for Solving Convex Feasibility Problems. SIAM Review, 38 (3). pp. 367-426.

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      Abstract

      Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: angle between two subspaces, averaged mapping, Cimmino's method, computerized tomography, convex feasibility problem, convex function, convex inequalities, convex programming, convex set, Fejer monotone sequence, firmly nonexpansive mapping, Hilbert space, image recovery, iterative method, Kaczmarz's method, linear convergence, linear feasibility problem, linear inequalities, nonexpansive mapping, orthogonal projection, projection algorithm, projection method, Slater point, subdifferential, subgradient, subgradient algorithm, successive projections
      Subjects: 92-xx Biology and other natural sciences, behavioral sciences > 92Cxx Physiological, cellular and medical topics
      49-xx Calculus of variations and optimal control; optimization > 49Mxx Methods of successive approximations
      65-xx Numerical analysis > 65Jxx Numerical analysis in abstract spaces
      65-xx Numerical analysis > 65Kxx Mathematical programming, optimization and variational techniques
      52-xx Convex and discrete geometry > 52Axx General convexity
      65-xx Numerical analysis > 65Fxx Numerical linear algebra
      46-xx Functional analysis > 46Cxx Inner product spaces and their generalizations, Hilbert spaces
      90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
      26-xx Real functions > 26Bxx Functions of several variables
      65-xx Numerical analysis
      47-xx Operator theory > 47Hxx Nonlinear operators and their properties
      41-xx Approximations and expansions > 41Axx Approximations and expansions
      47-xx Operator theory > 47Nxx Miscellaneous applications of operator theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 14 Jan 2015 09:05
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/100

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