dc.contributor.advisor | Russell, Luke Prof. Dr. | |
dc.contributor.author | Martins, Anna-Lena | |
dc.date.accessioned | 2019-07-01T08:40:40Z | |
dc.date.available | 2019-07-01T08:40:40Z | |
dc.date.issued | 2019-07-01 | |
dc.identifier.uri | http://hdl.handle.net/21.11130/00-1735-0000-0003-C14C-E | |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7539 | |
dc.language.iso | eng | de |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject.ddc | 510 | de |
dc.title | Local and Global Analysis of Relaxed Douglas-Rachford for Nonconvex Feasibility Problems | de |
dc.type | doctoralThesis | de |
dc.contributor.referee | Russell, Luke Prof. Dr. | |
dc.date.examination | 2019-03-19 | |
dc.description.abstracteng | This thesis investigates the local and global convergence analysis of the relaxed
Douglas-Rachford method. This algorithm, which was first proposed over a decade
ago, has become a standard procedure in applications. Convergence results for this
algorithm are limited either to convex feasibility or consistent nonconvex feasibility
with strong assumptions on the regularity of the underlying sets. After discussing
feasibility problems and projection methods to solve these in general, we investigate
the relaxed Douglas-Rachford method in detail for inconsistent and nonconvex
feasibility problems. By introducing a new type of regularity of sets, called superregularity
at a distance, we establish sufficient conditions for local linear convergence
of the corresponding sequence for the method of relaxed Douglas-Rachford
subsuming already existing results in the literature. We analyze a cyclic relaxed
Douglas-Rachford scheme and state convergence results for closed and convex sets,
by considering many-set feasibility problems. We then apply the theory developed
to the famous phase retrieval problem and discuss the numerical performance of
the algorithms. | de |
dc.contributor.coReferee | Hohage, Thorsten Prof. Dr | |
dc.subject.eng | subtransversality | de |
dc.subject.eng | nonconvex | de |
dc.subject.eng | relaxed Douglas-Rachford | de |
dc.subject.eng | metric subregularity | de |
dc.subject.eng | linear convergence | de |
dc.subject.eng | fixed point | de |
dc.subject.eng | relaxed averaged alternating reflections | de |
dc.subject.eng | projection | de |
dc.subject.eng | inconsistent feasibility problem | de |
dc.subject.eng | super-regular | de |
dc.subject.eng | phase retrieval | de |
dc.subject.eng | cyclic relaxed Douglas-Rachford | de |
dc.identifier.urn | urn:nbn:de:gbv:7-21.11130/00-1735-0000-0003-C14C-E-9 | |
dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
dc.subject.gokfull | Mathematics (PPN61756535X) | de |
dc.identifier.ppn | 166829205X | |