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Projection Algorithms and Monotone Operators

Bauschke, Heinz H. (1996) Projection Algorithms and Monotone Operators. PhD thesis, Simon Fraser University.

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      Abstract

      This thesis consists of two parts: In Part I, projection algorithms for solving convex feasibility problems in Hilbert space are studied. Powerful techniques from Convex Analysis are employed within a very general framework that covers and extends many well-known results. Ostensibly different looking conditions sufficient for linear convergence are shown to be special instances of regularity --- a concept new in this context. Numerous examples, including subgradient algorithms, are presented. Several notions of monotonicity of operators on Banach spaces are analyzed in Part~II. Utilizing Convex and Functional Analysis, it is shown that for a bounded linear positive semi-definite operator, all these ``monotonicities'' coincide with the monotonicity of the conjugate operator. Moreover, monotonicity of the conjugate operator is automatic in many classical Banach spaces but not in spaces containing a complemented copy of the space of absolutely convergent sequences.

      Item Type: Thesis (PhD)
      Additional Information: pubdom FALSE
      Subjects: UNSPECIFIED
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 11 Jun 2013 14:26
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/173

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