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Selective linearization for multi-block convex optimization

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TitleInfo
Title
Selective linearization for multi-block convex optimization
Name (type = personal)
NamePart (type = family)
Du
NamePart (type = given)
Yu
NamePart (type = date)
1987-
DisplayForm
Yu Du
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Eckstein
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Jonathan
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Jonathan Eckstein
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Advisory Committee
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chair
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Ruszczynski
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Andrzej
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Andrzej Ruszczynski
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Advisory Committee
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internal member
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Lin
NamePart (type = given)
Xiaodong
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Xiaodong Lin
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Advisory Committee
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internal member
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Boros
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Endre
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Endre Boros
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Advisory Committee
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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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Rutgers University
Role
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degree grantor
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NamePart
Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2017
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2017-05
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2017
Place
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xx
Language
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eng
Abstract (type = abstract)
We consider the problem of minimizing a sum of several convex non-smooth functions. In this thesis, we introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple proximal steps. The algorithm is a form of multiple operator splitting in which the order of processing partial functions is not fixed, but rather determined in the course of calculations. It proposes one of the first operator-splitting type methods which are globally convergent for an arbitrary number of operators without artificial duplication of variables. This algorithm is a multi-block extension of the alternating linearization (ALIN) method for solving structured non-smooth convex optimization problems. Global convergence is proved and estimates of the convergence rate are derived. Specifically, under a strong convexity condition, the number of iterations needed to achieve solution accuracy ε is of order O(ln(1/ε)/ε). The convergence rate analysis technique invented by us can also be used to derive the rate of convergence of the classical bundle method and ALIN method, for which no convergence rate estimate has been available so far. We report results of extensive comparison experiments in structured regularization problems such as large-scale fused lasso regularization problems and overlapping group lasso problems. The numerical results demonstrate the efficacy and accuracy of the method.
Subject (authority = RUETD)
Topic
Operations Research
Subject (authority = ETD-LCSH)
Topic
Mathematical optimization
Subject (authority = ETD-LCSH)
Topic
Nonsmooth optimization
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_7984
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electronic resource
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application/pdf
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Extent
1 online resource (xii, 74 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Yu Du
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T34X5BN6
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Du
GivenName
Yu
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2017-04-11 11:34:26
AssociatedEntity
Name
Yu Du
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
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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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2017-04-11T11:11:47
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