An inexact [ell] sub(1) penalty SQP algorithm for PDE-constrained optimization with an application to shape optimization in linear elasticity

We develop an optimization algorithm which is able to deal with inexact evaluations of the objective function. The proposed algorithm employs sequential quadratic programming with a line search that uses the [ell] sub(1) penalty function for an Armijo-like condition. Both the objective gradient comp...

Full description

Saved in:
Bibliographic Details
Published in:Optimization methods & software Vol. 28; no. 5; pp. 943 - 968
Main Authors: Hess, Wolfgang, Ulbrich, Stefan
Format: Journal Article
Language:English
Published: 01.10.2013
Subjects:
Algorithms
Iterative methods
Mathematical analysis
Mathematical models
Optimization
Partial differential equations
Searching
Shape optimization
Solvers
ISSN:1055-6788, 1029-4937
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We develop an optimization algorithm which is able to deal with inexact evaluations of the objective function. The proposed algorithm employs sequential quadratic programming with a line search that uses the [ell] sub(1) penalty function for an Armijo-like condition. Both the objective gradient computations for the quadratic subproblems and the objective function computations for the line search admit some inexactness which is controlled by the algorithm. We prove convergence results for the presented algorithm under suitable assumptions. The kind of optimization problems handled by the algorithm arises, for example, when we apply iterative solvers in the evaluation of the reduced objective function of a shape optimization problem subject to the linear elasticity equations. In the second part of this paper, we present an application of the algorithm to the shape optimization of steel profiles using nested iterations with adaptively refined meshes. It is shown how the inexactness in the algorithm translates to an acceptable residual of the state and adjoint state solutions in the iterative solver. We look at three different stopping criteria for the outer iterations. Numerical results are presented.
AbstractList We develop an optimization algorithm which is able to deal with inexact evaluations of the objective function. The proposed algorithm employs sequential quadratic programming with a line search that uses the [ell] sub(1) penalty function for an Armijo-like condition. Both the objective gradient computations for the quadratic subproblems and the objective function computations for the line search admit some inexactness which is controlled by the algorithm. We prove convergence results for the presented algorithm under suitable assumptions. The kind of optimization problems handled by the algorithm arises, for example, when we apply iterative solvers in the evaluation of the reduced objective function of a shape optimization problem subject to the linear elasticity equations. In the second part of this paper, we present an application of the algorithm to the shape optimization of steel profiles using nested iterations with adaptively refined meshes. It is shown how the inexactness in the algorithm translates to an acceptable residual of the state and adjoint state solutions in the iterative solver. We look at three different stopping criteria for the outer iterations. Numerical results are presented.
Author Hess, Wolfgang
Ulbrich, Stefan
Author_xml – sequence: 1
  givenname: Wolfgang
  surname: Hess
  fullname: Hess, Wolfgang
– sequence: 2
  givenname: Stefan
  surname: Ulbrich
  fullname: Ulbrich, Stefan
BookMark eNqNz8tKAzEUBuAgCl7fwEWWuph6MrnNLEu9QkFFXYmUND3RyDQZJyla38F3dkrduNLVOfx8_4GzSzZDDEjIIYMBgwpOGEipdFUNSmBsoGQflhtkh0FZF6LmenO1S1mszDbZTekVAAQTaod8DQP1AT-MzfQRm-aJpsX0iB3TFoNp8pLe3d5Q0zzHzueXOXWxozenZ4WNIeXO9M0ZjW32c_9pso-BvveMmkBN2zberrMcaXoxLf6WPtCm75uOYmNS9tbn5T7ZcqZJePAz98jD-dn96LIYX19cjYbjomW8hILVWgmt7YzDVPMSUZXOIdcKjavQonXCWW4VwlRZqOXMcqnYDByg1XXl-B45Wt9tu_i2wJQnc59s_74JGBdpwrQQmoGW8D8Ksub131SISjO1wv-jsiyBfwN0I5YC
ContentType Journal Article
DBID 7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1080/10556788.2011.651082
DatabaseName Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
Computer and Information Systems Abstracts
Computer and Information Systems Abstracts
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1029-4937
EndPage 968
GroupedDBID .4S
.7F
.DC
.QJ
0BK
0R~
123
29N
30N
4.4
5VS
7SC
8FD
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABDBF
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGEJ
ACGFS
ACIWK
ACTIO
ACUHS
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AMVHM
AQRUH
ARCSS
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
DU5
EAP
EBS
EDO
EMK
EPL
EST
ESX
E~A
E~B
F5P
GTTXZ
H13
HF~
HZ~
H~P
I-F
IPNFZ
J.P
JQ2
KYCEM
L7M
L~C
L~D
M4Z
NA5
NY~
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TTHFI
TUROJ
TUS
TWF
UT5
UU3
ZGOLN
~S~
AQTUD
ID FETCH-LOGICAL-p1320-1976477cd30b732ee62ffe376eaf8ececf4fc3c6e0b6c095dc3561d0f0ec798f3
ISSN 1055-6788
IngestDate Sun Nov 09 13:21:08 EST 2025
Fri Sep 05 07:40:56 EDT 2025
Wed Oct 01 14:56:39 EDT 2025
Thu Oct 02 09:48:18 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 5
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-p1320-1976477cd30b732ee62ffe376eaf8ececf4fc3c6e0b6c095dc3561d0f0ec798f3
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ObjectType-Article-1
ObjectType-Feature-2
PQID 1448715220
PQPubID 23500
PageCount 26
ParticipantIDs proquest_miscellaneous_1744710750
proquest_miscellaneous_1744705939
proquest_miscellaneous_1448716059
proquest_miscellaneous_1448715220
PublicationCentury 2000
PublicationDate 20131001
PublicationDateYYYYMMDD 2013-10-01
PublicationDate_xml – month: 10
  year: 2013
  text: 20131001
  day: 01
PublicationDecade 2010
PublicationTitle Optimization methods & software
PublicationYear 2013
SSID ssj0004146
Score 1.9569662
Snippet We develop an optimization algorithm which is able to deal with inexact evaluations of the objective function. The proposed algorithm employs sequential...
SourceID proquest
SourceType Aggregation Database
StartPage 943
SubjectTerms Algorithms
Iterative methods
Mathematical analysis
Mathematical models
Optimization
Partial differential equations
Searching
Shape optimization
Solvers
Title An inexact [ell] sub(1) penalty SQP algorithm for PDE-constrained optimization with an application to shape optimization in linear elasticity
URI https://www.proquest.com/docview/1448715220
https://www.proquest.com/docview/1448716059
https://www.proquest.com/docview/1744705939
https://www.proquest.com/docview/1744710750
Volume 28
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor and Francis Online Journals
  customDbUrl:
  eissn: 1029-4937
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0004146
  issn: 1055-6788
  databaseCode: TFW
  dateStart: 19920101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3bjtMwELXKwgM8IK7iLiNRCVQFcq3jx4q22odVt4hWWwmhynHG20rdpDTt0p_gT_hIxrGzTVnELg-8RJU1StTO6cxxPDOHkDeSpWnsSe7g9sd3Qj-RToKJ1omlSkLBI8WVLMUm2GAQTyZ82Gj8rHphzhcsy-Ltli__q6txDZ2tW2f_wd0XN8UF_IxOxyu6Ha_XcnxH1y7CVvc-NqOy_SbqtopNoicy6XcAS8BbIPX-_GnYEovTfDVfz87KasNht-dIzRe1bAQS0RzDyZnt06ya4Fq1E2_NW4uZWMK-5Txrae4qVi1Aaq6rttd7Z8fHdWOjYF2UCCwwJXwXu2rcQzCK7if5Qp0Km2JxfbxIMHrPbJGasvi2ry68XRFcFW3dSHc-GF2_92DXfC17ZybBVCHaj2tQjGrxlpsZTzZ1c6PQcykrmDLKUgoUH2bmtrYxGBnZo_0h3IPjaX98dDQd9SajZtBffnO0Qpk-yW8GXYOWG-SmzyKuCwhH_ZNdF67tZau-VNWoGbsf_vToS8m_ZDSje-Su3YrQjoHQfdKA7AG5UxtQ-ZD86GTUgol-QSh9pQikt947akFEEUT0AkQUQUR_AxGtQ4NqEFGR0RqI6DqnJYj2LecZNSCiOxA9IuN-b_Tx0LECHs6y7Mz3kOuGjMk0cBMW-ABtXynAlAZCxSBBqlDJQLbBTdoSuX4qA6TzqatckIzHKnhMDrI8gyeEegmXkCQJA4F7WpmKOFRpCAqYD6kr46fkdfVrTjFA6lMvkUG-KXBvi3tyZKm-e5UN7uz5X2xYGDItgHmVjadZ-LNr2Dwnt3f_ihfkYL3awEtyS56v58XqVQmuXypxsPk
linkProvider Taylor & Francis
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+inexact+%5Bell%5D+sub%281%29+penalty+SQP+algorithm+for+PDE-constrained+optimization+with+an+application+to+shape+optimization+in+linear+elasticity&rft.jtitle=Optimization+methods+%26+software&rft.au=Hess%2C+Wolfgang&rft.au=Ulbrich%2C+Stefan&rft.date=2013-10-01&rft.issn=1055-6788&rft.eissn=1029-4937&rft.volume=28&rft.issue=5&rft.spage=943&rft.epage=968&rft_id=info:doi/10.1080%2F10556788.2011.651082&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1055-6788&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1055-6788&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1055-6788&client=summon