• SIGMAOPT SEMINAR/OCANA SEMINAR
  • Speaker: Robert Hesse, Institute for Numerical and Applied Mathematics, University of Goettingen
  • Title: Simple algorithms for nonconvex feasibility: analysis and some convergence results
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: WestGrid
  • Time and Date: 10:00 am, Fri, 5th Oct 2012
  • Abstract:

    In this talk projection algorithms for solving (nonconvex) feasibility problems in Euclidian spaces are considered. Of special interest are the Method of Alternating Projections (MAP) and the Averaged Alternating Reflection Algorithm (AAR) which cover some of the state of the art algorithms for our intended application, the phase retrieval problem. In the case of convex feasibility, firm nonexpansiveness of projection mappings is a global property that yields global convergence of MAP, and, for consistent problems, AAR. Based on epsilon-delta-regularity of sets (Bauschke, Luke, Phan, Wang 2012) a relaxed local version of firm nonexpansiveness with respect to the intersection is introduced for consistent feasibility problems. This combined with a type of coercivity condition, which relates to the regularity of the intersection, yields local linear convergence of MAP for a wide class of nonconvex problems, and even local linear convergence of AAR in more limited nonconvex settings.


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