Generalized self-concordant Hessian-barrier algorithms
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2693 | |
dc.contributor.author | Dvurechensky, Pavel | |
dc.contributor.author | Staudigl, Mathias | |
dc.contributor.author | Uribe , Casar A. | |
dc.date.accessioned | 2022-06-30T12:42:34Z | |
dc.date.available | 2022-06-30T12:42:34Z | |
dc.date.issued | 2020 | |
dc.description.abstract | Many problems in statistical learning, imaging, and computer vision involve the optimization of a non-convex objective function with singularities at the boundary of the feasible set. For such challenging instances, we develop a new interior-point technique building on the Hessian-barrier algorithm recently introduced in Bomze, Mertikopoulos, Schachinger and Staudigl, [SIAM J. Opt. 2019 29(3), pp. 2100-2127], where the Riemannian metric is induced by a generalized selfconcordant function. This class of functions is sufficiently general to include most of the commonly used barrier functions in the literature of interior point methods. We prove global convergence to an approximate stationary point of the method, and in cases where the feasible set admits an easily computable self-concordant barrier, we verify worst-case optimal iteration complexity of the method. Applications in non-convex statistical estimation and Lp-minimization are discussed to given the efficiency of the method. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9343 | |
dc.identifier.uri | https://doi.org/10.34657/8381 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2693 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject | Non-convex optimization | eng |
dc.subject | Bregman divergence | eng |
dc.subject | generalized self-concordance | eng |
dc.subject | linear constraints | eng |
dc.subject.ddc | 510 | |
dc.title | Generalized self-concordant Hessian-barrier algorithms | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.extent | 42 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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