Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications
In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothin...
Gespeichert in:
| Veröffentlicht in: | IEEE transaction on neural networks and learning systems 2012-03, Vol.23 (3), p.399-411 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 411 |
|---|---|
| container_issue | 3 |
| container_start_page | 399 |
| container_title | IEEE transaction on neural networks and learning systems |
| container_volume | 23 |
| creator | Bian, Wei Chen, Xiaojun |
| description | In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN. |
| doi_str_mv | 10.1109/TNNLS.2011.2181867 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_crossref_primary_10_1109_TNNLS_2011_2181867</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>6123210</ieee_id><sourcerecordid>2597240521</sourcerecordid><originalsourceid>FETCH-LOGICAL-c413t-636d3b7fdbb903033a92f4955c69342c9f09cfb0a19d025f827bbc46e369dc0e3</originalsourceid><addsrcrecordid>eNqFkU1LxDAQhoMoKqt_QEGKIHjpmu82R1n8gmU9qOitpGniRtumJimiv966u67gxbnMkDzzwvAAcIDgGCEozu5ns-ndGEOExhjlKOfZBtjFiOMUkzzfXM_Z0w7YD-EFDsUh41Rsgx1Mc5gzmu2Ch7vGuTi37XMy072X9dDiu_OviXE-mbg2RC9tq6tk5tp0arug5jZ-JrddtI39lNG6Nnm0cZ6cd11t1eIh7IEtI-ug91d9BB4uL-4n1-n09upmcj5NFUUkppzwipSZqcpSQAIJkQIbKhhTXBCKlTBQKFNCiUQFMTM5zspSUa4JF5WCmozA6TK38-6t1yEWjQ1K17VstetDgRgmFDLE6P8oRIIzQRgf0OM_6IvrfTscUghMBOY5ZQOEl5DyLgSvTdF520j_MSQV34aKhaHi21CxMjQsHa2S-7LR1Xrlx8cAnKwAGZSsjZetsuGXYxxBuuAOl5zVWq-_OcIEI0i-ADLPoOc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>923926845</pqid></control><display><type>article</type><title>Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications</title><source>IEEE Electronic Library (IEL)</source><creator>Bian, Wei ; Chen, Xiaojun</creator><creatorcontrib>Bian, Wei ; Chen, Xiaojun</creatorcontrib><description>In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.</description><identifier>ISSN: 2162-237X</identifier><identifier>EISSN: 2162-2388</identifier><identifier>DOI: 10.1109/TNNLS.2011.2181867</identifier><identifier>PMID: 24808547</identifier><identifier>CODEN: ITNNAL</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Approximation methods ; Artificial intelligence ; Computer science; control theory; systems ; Connectionism. Neural networks ; Detection, estimation, filtering, equalization, prediction ; Differential equations ; Exact sciences and technology ; Image and signal restoration ; Information, signal and communications theory ; Input variables ; Mathematical model ; Mathematical models ; Models, Theoretical ; Neural networks ; Neural Networks (Computer) ; non-Lipschitz optimization ; Optimization ; Pattern recognition. Digital image processing. Computational geometry ; Signal and communications theory ; Signal, noise ; Smoothing methods ; smoothing neural network ; stationary point ; Studies ; Telecommunications and information theory ; variable selection</subject><ispartof>IEEE transaction on neural networks and learning systems, 2012-03, Vol.23 (3), p.399-411</ispartof><rights>2015 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Mar 2012</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c413t-636d3b7fdbb903033a92f4955c69342c9f09cfb0a19d025f827bbc46e369dc0e3</citedby><cites>FETCH-LOGICAL-c413t-636d3b7fdbb903033a92f4955c69342c9f09cfb0a19d025f827bbc46e369dc0e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6123210$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6123210$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=25610447$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/24808547$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Bian, Wei</creatorcontrib><creatorcontrib>Chen, Xiaojun</creatorcontrib><title>Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications</title><title>IEEE transaction on neural networks and learning systems</title><addtitle>TNNLS</addtitle><addtitle>IEEE Trans Neural Netw Learn Syst</addtitle><description>In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.</description><subject>Applied sciences</subject><subject>Approximation methods</subject><subject>Artificial intelligence</subject><subject>Computer science; control theory; systems</subject><subject>Connectionism. Neural networks</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Differential equations</subject><subject>Exact sciences and technology</subject><subject>Image and signal restoration</subject><subject>Information, signal and communications theory</subject><subject>Input variables</subject><subject>Mathematical model</subject><subject>Mathematical models</subject><subject>Models, Theoretical</subject><subject>Neural networks</subject><subject>Neural Networks (Computer)</subject><subject>non-Lipschitz optimization</subject><subject>Optimization</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Signal and communications theory</subject><subject>Signal, noise</subject><subject>Smoothing methods</subject><subject>smoothing neural network</subject><subject>stationary point</subject><subject>Studies</subject><subject>Telecommunications and information theory</subject><subject>variable selection</subject><issn>2162-237X</issn><issn>2162-2388</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><sourceid>EIF</sourceid><recordid>eNqFkU1LxDAQhoMoKqt_QEGKIHjpmu82R1n8gmU9qOitpGniRtumJimiv966u67gxbnMkDzzwvAAcIDgGCEozu5ns-ndGEOExhjlKOfZBtjFiOMUkzzfXM_Z0w7YD-EFDsUh41Rsgx1Mc5gzmu2Ch7vGuTi37XMy072X9dDiu_OviXE-mbg2RC9tq6tk5tp0arug5jZ-JrddtI39lNG6Nnm0cZ6cd11t1eIh7IEtI-ug91d9BB4uL-4n1-n09upmcj5NFUUkppzwipSZqcpSQAIJkQIbKhhTXBCKlTBQKFNCiUQFMTM5zspSUa4JF5WCmozA6TK38-6t1yEWjQ1K17VstetDgRgmFDLE6P8oRIIzQRgf0OM_6IvrfTscUghMBOY5ZQOEl5DyLgSvTdF520j_MSQV34aKhaHi21CxMjQsHa2S-7LR1Xrlx8cAnKwAGZSsjZetsuGXYxxBuuAOl5zVWq-_OcIEI0i-ADLPoOc</recordid><startdate>20120301</startdate><enddate>20120301</enddate><creator>Bian, Wei</creator><creator>Chen, Xiaojun</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QF</scope><scope>7QO</scope><scope>7QP</scope><scope>7QQ</scope><scope>7QR</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7TK</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>H8D</scope><scope>JG9</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P64</scope><scope>7X8</scope></search><sort><creationdate>20120301</creationdate><title>Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications</title><author>Bian, Wei ; Chen, Xiaojun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c413t-636d3b7fdbb903033a92f4955c69342c9f09cfb0a19d025f827bbc46e369dc0e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied sciences</topic><topic>Approximation methods</topic><topic>Artificial intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Connectionism. Neural networks</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>Differential equations</topic><topic>Exact sciences and technology</topic><topic>Image and signal restoration</topic><topic>Information, signal and communications theory</topic><topic>Input variables</topic><topic>Mathematical model</topic><topic>Mathematical models</topic><topic>Models, Theoretical</topic><topic>Neural networks</topic><topic>Neural Networks (Computer)</topic><topic>non-Lipschitz optimization</topic><topic>Optimization</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Signal and communications theory</topic><topic>Signal, noise</topic><topic>Smoothing methods</topic><topic>smoothing neural network</topic><topic>stationary point</topic><topic>Studies</topic><topic>Telecommunications and information theory</topic><topic>variable selection</topic><toplevel>online_resources</toplevel><creatorcontrib>Bian, Wei</creatorcontrib><creatorcontrib>Chen, Xiaojun</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Aluminium Industry Abstracts</collection><collection>Biotechnology Research Abstracts</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transaction on neural networks and learning systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bian, Wei</au><au>Chen, Xiaojun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications</atitle><jtitle>IEEE transaction on neural networks and learning systems</jtitle><stitle>TNNLS</stitle><addtitle>IEEE Trans Neural Netw Learn Syst</addtitle><date>2012-03-01</date><risdate>2012</risdate><volume>23</volume><issue>3</issue><spage>399</spage><epage>411</epage><pages>399-411</pages><issn>2162-237X</issn><eissn>2162-2388</eissn><coden>ITNNAL</coden><abstract>In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.</abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>24808547</pmid><doi>10.1109/TNNLS.2011.2181867</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 2162-237X |
| ispartof | IEEE transaction on neural networks and learning systems, 2012-03, Vol.23 (3), p.399-411 |
| issn | 2162-237X 2162-2388 |
| language | eng |
| recordid | cdi_crossref_primary_10_1109_TNNLS_2011_2181867 |
| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Approximation methods Artificial intelligence Computer science control theory systems Connectionism. Neural networks Detection, estimation, filtering, equalization, prediction Differential equations Exact sciences and technology Image and signal restoration Information, signal and communications theory Input variables Mathematical model Mathematical models Models, Theoretical Neural networks Neural Networks (Computer) non-Lipschitz optimization Optimization Pattern recognition. Digital image processing. Computational geometry Signal and communications theory Signal, noise Smoothing methods smoothing neural network stationary point Studies Telecommunications and information theory variable selection |
| title | Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T18%3A09%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Smoothing%20Neural%20Network%20for%20Constrained%20Non-Lipschitz%20Optimization%20With%20Applications&rft.jtitle=IEEE%20transaction%20on%20neural%20networks%20and%20learning%20systems&rft.au=Bian,%20Wei&rft.date=2012-03-01&rft.volume=23&rft.issue=3&rft.spage=399&rft.epage=411&rft.pages=399-411&rft.issn=2162-237X&rft.eissn=2162-2388&rft.coden=ITNNAL&rft_id=info:doi/10.1109/TNNLS.2011.2181867&rft_dat=%3Cproquest_RIE%3E2597240521%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=923926845&rft_id=info:pmid/24808547&rft_ieee_id=6123210&rfr_iscdi=true |