An interior proximal gradient method for nonconvex optimization

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth objective functions and proximal algorithms cannot handle co...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org
Main Authors: De Marchi, Alberto, Themelis, Andreas
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 29.01.2024
Subjects:
Algorithms
Asymptotic properties
Optimization
ISSN:2331-8422
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth objective functions and proximal algorithms cannot handle complicated constraints, their combined usage is shown to successfully compensate the respective shortcomings. We provide a theoretical characterization of the algorithm and its asymptotic properties, deriving convergence results for fully nonconvex problems, thus bridging the gap with previous works that successfully addressed the convex case. Our interior proximal gradient algorithm benefits from warm starting, generates strictly feasible iterates with decreasing objective value, and returns after finitely many iterations a primal-dual pair approximately satisfying suitable optimality conditions. As a byproduct of our analysis of proximal gradient iterations we demonstrate that a slight refinement of traditional backtracking techniques waives the need for upper bounding the stepsize sequence, as required in existing results for the nonconvex setting.
AbstractList We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth objective functions and proximal algorithms cannot handle complicated constraints, their combined usage is shown to successfully compensate the respective shortcomings. We provide a theoretical characterization of the algorithm and its asymptotic properties, deriving convergence results for fully nonconvex problems, thus bridging the gap with previous works that successfully addressed the convex case. Our interior proximal gradient algorithm benefits from warm starting, generates strictly feasible iterates with decreasing objective value, and returns after finitely many iterations a primal-dual pair approximately satisfying suitable optimality conditions. As a byproduct of our analysis of proximal gradient iterations we demonstrate that a slight refinement of traditional backtracking techniques waives the need for upper bounding the stepsize sequence, as required in existing results for the nonconvex setting.
Author De Marchi, Alberto
Themelis, Andreas
Author_xml – sequence: 1
  givenname: Alberto
  surname: De Marchi
  fullname: De Marchi, Alberto
– sequence: 2
  givenname: Andreas
  surname: Themelis
  fullname: Themelis, Andreas
BookMark eNotj01LAzEURYMoWGt_gLsB11NfXr5XUopWoeCm-5ImqaZ0kppJy-Cvd0BXd3HgnnvvyHXKKRDyQGHOtRDwZMsQL3NE0HMAZcwVmSBjtNUc8ZbM-v4AACgVCsEm5HmRmphqKDGX5lTyEDt7bD6L9TGk2nShfmXf7Ec4elxOlzA0-VRjF39sjTndk5u9PfZh9p9Tsnl92Szf2vXH6n25WLdWILTScS61cZLuDBoeJFVUKBqMM0iDc8wo6632Ulnmd8JpBcAlaASlqGeUTcnjX-048fsc-ro95HNJo3GL0igEOh5mvxyeS70
ContentType Paper
Copyright 2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOI 10.48550/arxiv.2208.00799
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Materials Science & Engineering
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-LOGICAL-a520-6c44689c61b9294e6171571e9c921ecc397ada8d67a3db5c8700460820771d313
IEDL.DBID BENPR
IngestDate Mon Jun 30 09:17:48 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a520-6c44689c61b9294e6171571e9c921ecc397ada8d67a3db5c8700460820771d313
Notes SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
OpenAccessLink https://www.proquest.com/docview/2697201220?pq-origsite=%requestingapplication%
PQID 2697201220
PQPubID 2050157
ParticipantIDs proquest_journals_2697201220
PublicationCentury 2000
PublicationDate 20240129
PublicationDateYYYYMMDD 2024-01-29
PublicationDate_xml – month: 01
  year: 2024
  text: 20240129
  day: 29
PublicationDecade 2020
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2024
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 1.8589628
SecondaryResourceType preprint
Snippet We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Algorithms
Asymptotic properties
Optimization
Title An interior proximal gradient method for nonconvex optimization
URI https://www.proquest.com/docview/2697201220
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpZ3PS8MwFMeDbgqe_I0_5sjBa13TtElzGiobCjqKDpmnkSaZFFw72zn25_uSdXoQvHgsgTbkhddP3vvmPYQufWZUYMLYUwDDXqgnyksjKjzGlCTBxKfG1el-eeCDQTwaiaQOuFW1rHLtE52j1oWyMfJOwAQPbB7I784-PNs1ymZX6xYam6hpK5WFDdS86Q2Sp-8oS8A4MDNdpTNd8a6OLJfZ4greY0WUXIhfTtj9Wfq7_53THmomcmbKfbRh8gO07RSdqjpE3esc21oQZVaU2IpVsql8x2-lk3jN8apzNAZkxXmRO-35EhfgP6b1xcwjNOz3hrd3Xt0twZORPQIqONjFQjGSAvGEBsiERJwYoURAwE7AHVLLWDMuqU4jMI27NwoAwDnRlNBj1IDvmROEw1SFMqZM-VKGPtWSTLSiKbCdH0kdm1PUWi_HuN7x1fhnLc7-Hj5HOwGAgQ1jBKKFGvPy01ygLbWYZ1XZrg3YthrMZ3hK7h-T1y8616ix
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LTwIxEJ4gaPTkOz5Qe9Dj6m67rx4MMSqBgIREYriRblvMJvJwQcQf5X90WkAPJt44eN5kt512Z76Z-WYG4NwNtaTajx2JYNjxVVc6ScC4E4ZSeLTrMm37dD_Vo0Yjbrd5Mwefi1oYQ6tc6ESrqNVAmhj5FQ15RE0eyC0NXx0zNcpkVxcjNGbXoqY_3tFlG11X7_B8Lygt37duK858qoAjAuMqSXSAYi5DL0Fk4Gu04F4QeZpLTj3cD9pnoUSswkgwlQS4BVtfiYYyijzFPIavXYGCb5S_ZQo-fod0aBghQGez3KntFHYlsmk6ucRFG8ZmxPkvjW_NWHnznwlgCwpNMdTZNuR0fwfWLFtVjnahdNMnps9Flg4yYog4aU-8kOfM0tfGZDYVmyAcJ_1B3_Lqp2SAurE3Lzrdg9YylrwPefyePgDiJ9IXMQulK4TvMiW8rpIsQdzqBkLF-hCKC-l35n_zqPMj-qO_H5_BeqX1UO_Uq43aMWxQBEAmXEN5EfLj7E2fwKqcjNNRdmpvDoHOkg_qC_pn_K0
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+interior+proximal+gradient+method+for+nonconvex+optimization&rft.jtitle=arXiv.org&rft.au=De+Marchi%2C+Alberto&rft.au=Themelis%2C+Andreas&rft.date=2024-01-29&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2208.00799