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Alternating linearization for structured regularization problems
Descriptive
TitleInfo
Title
Alternating linearization for structured regularization problems
Name
(type = personal)
NamePart
(type = family)
Pham
NamePart
(type = given)
Minh
DisplayForm
Minh Pham
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author
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Ruszczy´nski
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Andrzej
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Andrzej Ruszczy´nski
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Advisory Committee
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chair
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Lin
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Xiaodong
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Xiaodong Lin
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Advisory Committee
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co-chair
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(type = family)
Alizadeh
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Farid
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Farid Alizadeh
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Advisory Committee
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internal member
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(type = family)
Jeong
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Myong
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Myong Jeong
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Advisory Committee
Role
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internal member
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Dentcheva
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Darinka
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Darinka Dentcheva
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Advisory Committee
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outside member
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NamePart
Rutgers University
Role
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degree grantor
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NamePart
Graduate School - New Brunswick
Role
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school
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Text
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theses
OriginInfo
DateCreated
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2014
DateOther
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(type = degree)
2014-05
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
We adapt the alternating linearization method for proximal decomposition to structured regularization problems. The method is related to two well-known operator splitting methods, the Douglas-Rachford and the Peaceman-Rachford method, but it has descent properties with respect to the objective function. Its convergence mechanism is related to that of bundle methods of nonsmooth optimization. A block coordinate descent method is developed to facilitate fast convergence. We also discuss implementation for large problems, with the use of specialized algorithms and sparse data structures. We present numerical results for several synthetic and real-world examples, including a three-dimensional fused lasso problem, which illustrate the scalability, efficacy, and accuracy of the method. We further extend the alternating linearization framework to the structured regularization problems with non-convex penalties. In this framework, the non-convex part of the objective function is approximated via a linear model. Therefore, in each iteration, the method solves a structured regularization problem. We present several numerical studies with synthetic data and cancer research data.
Subject
(authority = RUETD)
Topic
Operations Research
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_5575
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 71 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Minh Pham
Subject
(authority = ETD-LCSH)
Topic
Mathematical optimization
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3T72FRZ
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
(type = personal)
Name
FamilyName
Pham
GivenName
Minh
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2014-04-24 17:30:35
AssociatedEntity
Name
Minh Pham
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
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ContentModel
ETD
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windows xp
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