Local and Global Analysis of Relaxed Douglas-Rachford for Nonconvex Feasibility Problems

Martins, Anna-Lena

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

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

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