First-order and second-order optimality conditions for nonsmooth constrained problems via convolution smoothing

This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order...

Full description

Saved in:
Bibliographic Details
Published in:Optimization Vol. 60; no. 1-2; pp. 253 - 275
Main Authors: Eberhard, Andrew C., Mordukhovich, Boris S.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 01.01.2011
Taylor & Francis LLC
Subjects:
constrained optimization
Constraints
Construction
Convolution
Derivatives
Differential equations
Envelopes
first-order and second-order optimality conditions
generalized differentiation
Mathematical problems
Optimization
Optimization algorithms
Regularization
Smoothing
Studies
variational analysis
ISSN:0233-1934, 1029-4945
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions.
AbstractList This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions. [PUBLICATION ABSTRACT]
This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way, we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials and second-order subdifferentials defined via coderivatives of first-order constructions.
Author Eberhard, Andrew C.
Mordukhovich, Boris S.
Author_xml – sequence: 1
  givenname: Andrew C.
  surname: Eberhard
  fullname: Eberhard, Andrew C.
  organization: School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology
– sequence: 2
  givenname: Boris S.
  surname: Mordukhovich
  fullname: Mordukhovich, Boris S.
  email: boris@math.wayne.edu.
  organization: Department of Mathematics , Wayne State University
BookMark eNqFkUtP3TAQha2KSr1Q_gGLiFU3Ab-SOGxQhXhJSGzatTWxndbIsS-2L9X999gKbFiUlaWZ74zPzDlEBz54g9AJwWcEC3yOKWNkZPyM4lLqKB0I-4I2BNOx5SPvDtCmIm1lvqHDlJ4wpqSnfIPCjY0ptyFqExvwuklGBa_fCmGb7QLO5n1Tqzbb4FMzh9gUB2kJIf-tjZQjWG90s41hcmZJzYuF2ngJblc1zcpa_-c7-jqDS-b47T1Cv2-uf13dtQ-Pt_dXPx9axTjLraYUG4aHHjCl0NFunARMWmvSTwpAd2RQI9ZcTTCNvBd6YIKWHaFnQ6fEzI7Qj3VusfS8MynLxSZlnANvwi5JwukoBtF3XUFPP6BPYRd9cSdF-UcIynGBLlZIxZBSNLNUNkPdre7uJMGyRiHfo5A1CrlGUcT8g3gby13j_jPZ5Sqzvpx8gX8hOi0z7F2IcwSvbJLsvxNeASbAo4w
CODEN OPTZDQ
CitedBy_id crossref_primary_10_1155_2011_167160
crossref_primary_10_1080_02331934_2018_1522537
crossref_primary_10_1007_s10107_018_1238_8
Cites_doi 10.1090/S0273-0979-1992-00266-5
10.1137/S1052623400377153
10.1090/S0002-9947-96-01544-9
10.1137/07068059X
10.1137/0324061
10.1137/0322017
10.1023/B:SVAN.0000023398.73288.82
10.1006/jmaa.1995.1247
10.1007/978-1-4613-3341-8_4
10.1137/S1052623494278839
10.1007/BF02207780
10.1016/S0294-1449(16)30214-1
10.1007/BF01585170
10.1007/s10107-007-0123-7
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2011
Copyright Taylor & Francis Group Jan 2011
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2011
– notice: Copyright Taylor & Francis Group Jan 2011
DBID AAYXX
CITATION
7SC
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
DOI 10.1080/02331934.2010.522713
DatabaseName CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
Aerospace Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Aerospace Database
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Aerospace Database

Aerospace Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1029-4945
EndPage 275
ExternalDocumentID 2267863291
10_1080_02331934_2010_522713
522713
Genre Feature
GroupedDBID .7F
.DC
.QJ
0BK
0R~
123
29N
30N
4.4
5VS
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGEJ
ACGFS
ACIWK
ACTCW
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGCQS
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AMVHM
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CAG
CCCUG
CE4
COF
CS3
DKSSO
DU5
EBS
EJD
E~A
E~B
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
M4Z
NA5
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TTHFI
TUROJ
TWF
UT5
UU3
ZGOLN
~S~
07G
1TA
AAIKQ
AAKBW
AAYXX
ACAGQ
ACGEE
AEUMN
AGLEN
AGROQ
AHMOU
ALCKM
AMEWO
AMXXU
BCCOT
BPLKW
C06
CITATION
CRFIH
DMQIW
DWIFK
IVXBP
LJTGL
NUSFT
QCRFL
TAQ
TFMCV
TOXWX
UB9
UU8
V3K
V4Q
7SC
7TB
8FD
FR3
H8D
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c343t-d220e3076a022a5259b8abddd16bcaad517c90d4cbab9468d7382023a6375c8f3
IEDL.DBID TFW
ISICitedReferencesCount 6
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000287214500017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0233-1934
IngestDate Sun Nov 09 09:58:48 EST 2025
Mon Nov 10 02:55:08 EST 2025
Tue Nov 18 22:11:33 EST 2025
Sat Nov 29 06:01:38 EST 2025
Mon Oct 20 23:46:25 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1-2
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c343t-d220e3076a022a5259b8abddd16bcaad517c90d4cbab9468d7382023a6375c8f3
Notes SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
PQID 851788240
PQPubID 27961
PageCount 23
ParticipantIDs proquest_journals_851788240
proquest_miscellaneous_1429878655
crossref_citationtrail_10_1080_02331934_2010_522713
informaworld_taylorfrancis_310_1080_02331934_2010_522713
crossref_primary_10_1080_02331934_2010_522713
PublicationCentury 2000
PublicationDate 1/1/2011
2011-01-00
20110101
PublicationDateYYYYMMDD 2011-01-01
PublicationDate_xml – month: 01
  year: 2011
  text: 1/1/2011
  day: 01
PublicationDecade 2010
PublicationPlace Philadelphia
PublicationPlace_xml – name: Philadelphia
PublicationTitle Optimization
PublicationYear 2011
Publisher Taylor & Francis Group
Taylor & Francis LLC
Publisher_xml – name: Taylor & Francis Group
– name: Taylor & Francis LLC
References Attouch H (CIT0001) 1993; 10
CIT0020
CIT0012
Mifflin R (CIT0010) 1996; 73
Eberhard AC (CIT0005) 1998
Mordukhovich BS (CIT0014) 2006; 331
Eberhard AC (CIT0006) 2006; 13
Rockafellar RT (CIT0017) 2006; 317
CIT0003
CIT0002
Mordukhovich BS (CIT0013) 2006; 330
CIT0016
CIT0004
CIT0015
CIT0007
CIT0018
CIT0009
CIT0008
CIT0019
References_xml – ident: CIT0004
  doi: 10.1090/S0273-0979-1992-00266-5
– ident: CIT0015
  doi: 10.1137/S1052623400377153
– volume: 317
  volume-title: Grundlehren Series: Fundamental Principles of Mathematical Sciences
  year: 2006
  ident: CIT0017
– ident: CIT0016
  doi: 10.1090/S0002-9947-96-01544-9
– ident: CIT0007
  doi: 10.1137/07068059X
– volume: 331
  volume-title: Grundlehren Series: Fundamental Principles of Mathematical Sciences
  year: 2006
  ident: CIT0014
– ident: CIT0018
  doi: 10.1137/0324061
– ident: CIT0002
  doi: 10.1137/0322017
– ident: CIT0012
  doi: 10.1023/B:SVAN.0000023398.73288.82
– volume: 73
  start-page: 51
  year: 1996
  ident: CIT0010
  publication-title: Math. Program.
– volume: 13
  start-page: 647
  year: 2006
  ident: CIT0006
  publication-title: J. Convex Anal.
– ident: CIT0020
  doi: 10.1006/jmaa.1995.1247
– start-page: 111
  volume-title: Generalized Convexity, Generalized Monotonicity : Recent Results
  year: 1998
  ident: CIT0005
  doi: 10.1007/978-1-4613-3341-8_4
– ident: CIT0008
  doi: 10.1137/S1052623494278839
– volume: 330
  volume-title: Grundlehren Series: Fundamental Principles of Mathematical Sciences
  year: 2006
  ident: CIT0013
– ident: CIT0019
  doi: 10.1007/BF02207780
– volume: 10
  start-page: 289
  year: 1993
  ident: CIT0001
  publication-title: Ann. Inst. H. Poincaré. Anal. Non Linéare
  doi: 10.1016/S0294-1449(16)30214-1
– ident: CIT0003
  doi: 10.1007/BF01585170
– ident: CIT0009
  doi: 10.1007/s10107-007-0123-7
SSID ssj0021624
Score 1.8680531
Snippet This article mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained...
SourceID proquest
crossref
informaworld
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 253
SubjectTerms constrained optimization
Constraints
Construction
Convolution
Derivatives
Differential equations
Envelopes
first-order and second-order optimality conditions
generalized differentiation
Mathematical problems
Optimization
Optimization algorithms
Regularization
Smoothing
Studies
variational analysis
Title First-order and second-order optimality conditions for nonsmooth constrained problems via convolution smoothing
URI https://www.tandfonline.com/doi/abs/10.1080/02331934.2010.522713
https://www.proquest.com/docview/851788240
https://www.proquest.com/docview/1429878655
Volume 60
WOSCitedRecordID wos000287214500017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Journals Complete
  customDbUrl:
  eissn: 1029-4945
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0021624
  issn: 0233-1934
  databaseCode: TFW
  dateStart: 19850101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpR3LSgMxMEjxoAffYq1KBK_BfWQ32aOIxYMUDxV7WyaPhYJtxW37_U6S3dIiKijsYUkymyGZZ3YyQ8hNoZU1UZEwBcjkvKokUxFwhu4Q8MjGmQKfXf9JDAZyNCqe127xu7BK50NXIVGEl9WOuUHVbUTcLaoZJJyUh8AsNCCEL1uLmt9x5rD_uvK44txXtXUAzEG0d-e--ciGbtrIXPpFUnv109__P-IHZK8xPeldoJVDsmWnR2R3LSHhMZn1x2gNMp-Pk-I0tHb-smkaZiheJt5up641BHtRRJ9O8WUyw013HbUvO2ENbYrV1HQ5BtexbMichrE44wl56T8M7x9ZU5KB6ZSnc2aSJLIoFnJA3Q8Z-k5KgjLGxLnSACaLhS4iw7UCVfBcGpFKV6Ad8lRkWlbpKekgSvaMUFPFhZFWapkDz22lBBRoLYAQkYpEIrskbTej1E2-cof_Wxm3aU2b5SzdcpZhObuEraDeQ76OX8bL9X0u5_6cpApFTcr0Z9BeSxNlw_h1iQasQKeFR11yvepFjnW_YWBqZ4sana2kkMJdCD7_--Q9shNOt91zQTrzj4W9JNt6OR_XH1eeCz4B6dkE2Q
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1bSxwxFA6iQtsHbbXiemkj-Bo6l8wk8yjFRXG79GFF30JuAwu6K866v7_nJJlFKbYgwjwMSc4kJDm3zMl3CDltrPEuawpmNDA5b1vJTKY5A3dI88znldEBXX8kxmN5e9v8TtGEXQqrRB-6jUARQVYjc-NhdB8S9wP0DOycksfILLAgBOat3ahA1SJ8_mR4s_K58jrktUUKhiT97blXvvJCO73ALv1LVgcFNNx-h6F_JlvJ-qRncbt8IWt-tkM-PcMk3CXz4RQMQhYgOSn0Qzt0mV0qmIOEuQ-mO8XSGO9FYfx0Bi_3c1h3rOhC5gnvaMpX09HlVGPFMu10GttCj1_J9fB88vOCpawMzJa8XDBXFJkHyVBrUP-6AvfJSG2cc3ltrNauyoVtMset0abhtXSilJijXdelqKxsyz2yDkPy-4S6Nm-c9NLKWvPat0boBgwGLURmMlHIASn71VA2QZbj-O9U3iObpulUOJ0qTueAsBXVQ4Ts-E97-Xyh1SIclbQxr4kq_0162G8KlXi_U2DDCvBbeDYgJ6taYFr8E6Nnfv7Ugb9VNFLgneCDt3f-nXy4mPwaqdHl-OqQfIyH3fgckfXF45M_Jpt2uZh2j98CS_wBaHwJAw
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpR1da9swUJSujO6h67qWpt1aDfoq5g_Fkh_HWrPREPLQsb4JfRkCbRJiJ79_d5IdEsY26MAPRtJZh3Sf8umOkJvSGu-SMmNGA5PzupbMJJozcIc0T3w6NDpk1x-J8Vg-PpaTrVv8GFaJPnQdE0UEWY3MvXB1HxH3GdQMEE7OY2AWGBACy9a-Asu5QBp_qH5uXK60CGVtEYIhSH957g9f2VFOO6lLfxPVQf9Ub_8f82Ny1Nme9Esklndkz89OyJutjITvybyagjnIQkJOCtPQBh1m1zXMQb48B8OdYmuM9qKAPp3By_Mcdh07mlB3wjvaVatp6HqqsWPd0TmNY2HGU_Kjunv4-o11NRmYzXneMpdliQe5UGhQ_noIzpOR2jjn0sJYrd0wFbZMHLdGm5IX0olcYoV2XeRiaGWdn5F9QMmfE-rqtHTSSysLzQtfG6FLMBe0EIlJRCYHJO83Q9kuYTni_6TSPq9pt5wKl1PF5RwQtoFaxIQd_xgvt_dZteGgpI5VTVT-d9DLniZUx_mNAgtWgNfCkwH5tOkFlsX_MHrm56sGvK2slAJvBF-8fPJr8npyW6nR9_H9JTmMJ934fCD77XLlP5IDu26nzfIqMMQvQQMHtQ
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=First-order+and+second-order+optimality+conditions+for+nonsmooth+constrained+problems+via+convolution+smoothing&rft.jtitle=Optimization&rft.au=Eberhard%2C+Andrew+C&rft.au=Mordukhovich%2C+Boris+S&rft.date=2011-01-01&rft.issn=0233-1934&rft.eissn=1029-4945&rft.volume=60&rft.issue=1-2&rft.spage=253&rft.epage=275&rft_id=info:doi/10.1080%2F02331934.2010.522713&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0233-1934&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0233-1934&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0233-1934&client=summon