Orthogonal Invariance and Identifiability
Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are con...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on matrix analysis and applications 2014-01, Vol.35 (2), p.580-598 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 598 |
|---|---|
| container_issue | 2 |
| container_start_page | 580 |
| container_title | SIAM journal on matrix analysis and applications |
| container_volume | 35 |
| creator | Daniilidis, A. Drusvyatskiy, D. Lewis, A. S. |
| description | Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many active-set-type optimization algorithms. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/130916710 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1524239069</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3302648931</sourcerecordid><originalsourceid>FETCH-LOGICAL-c292t-cc0afe18418515b136fd11236c31187e7ac671aec1aaa36c39bf800a61bfbf4c3</originalsourceid><addsrcrecordid>eNo9kE9LxDAUxIMoWFcPfoOCpz1U30vaNDnK4p_Cwl70HF7TRLPUdk26wn57u6x4mmH4MQzD2C3CPaKoH1CARlkjnLEMQVdFjZKfswzU7Mtaq0t2ldIWAGWpMWPLTZw-x49xoD5vhh-KgQbrchq6vOncMAUfqA19mA7X7MJTn9zNny7Y-_PT2-q1WG9emtXjurBc86mwFsg7VCWqCqsWhfQdIhfSCkRVu5rsPI-cRSI6prr1CoAktr71pRULdnfq3cXxe-_SZLbjPs77ksGKl1xokHqmlifKxjGl6LzZxfBF8WAQzPEJ8_-E-AWRmU6X</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1524239069</pqid></control><display><type>article</type><title>Orthogonal Invariance and Identifiability</title><source>SIAM Journals</source><creator>Daniilidis, A. ; Drusvyatskiy, D. ; Lewis, A. S.</creator><creatorcontrib>Daniilidis, A. ; Drusvyatskiy, D. ; Lewis, A. S.</creatorcontrib><description>Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many active-set-type optimization algorithms. [PUBLICATION ABSTRACT]</description><identifier>ISSN: 0895-4798</identifier><identifier>EISSN: 1095-7162</identifier><identifier>DOI: 10.1137/130916710</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Eigenvalues ; Euclidean space ; Optimization algorithms ; Values</subject><ispartof>SIAM journal on matrix analysis and applications, 2014-01, Vol.35 (2), p.580-598</ispartof><rights>2014, Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c292t-cc0afe18418515b136fd11236c31187e7ac671aec1aaa36c39bf800a61bfbf4c3</citedby><cites>FETCH-LOGICAL-c292t-cc0afe18418515b136fd11236c31187e7ac671aec1aaa36c39bf800a61bfbf4c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,3184,27924,27925</link.rule.ids></links><search><creatorcontrib>Daniilidis, A.</creatorcontrib><creatorcontrib>Drusvyatskiy, D.</creatorcontrib><creatorcontrib>Lewis, A. S.</creatorcontrib><title>Orthogonal Invariance and Identifiability</title><title>SIAM journal on matrix analysis and applications</title><description>Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many active-set-type optimization algorithms. [PUBLICATION ABSTRACT]</description><subject>Eigenvalues</subject><subject>Euclidean space</subject><subject>Optimization algorithms</subject><subject>Values</subject><issn>0895-4798</issn><issn>1095-7162</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNo9kE9LxDAUxIMoWFcPfoOCpz1U30vaNDnK4p_Cwl70HF7TRLPUdk26wn57u6x4mmH4MQzD2C3CPaKoH1CARlkjnLEMQVdFjZKfswzU7Mtaq0t2ldIWAGWpMWPLTZw-x49xoD5vhh-KgQbrchq6vOncMAUfqA19mA7X7MJTn9zNny7Y-_PT2-q1WG9emtXjurBc86mwFsg7VCWqCqsWhfQdIhfSCkRVu5rsPI-cRSI6prr1CoAktr71pRULdnfq3cXxe-_SZLbjPs77ksGKl1xokHqmlifKxjGl6LzZxfBF8WAQzPEJ8_-E-AWRmU6X</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Daniilidis, A.</creator><creator>Drusvyatskiy, D.</creator><creator>Lewis, A. S.</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope></search><sort><creationdate>20140101</creationdate><title>Orthogonal Invariance and Identifiability</title><author>Daniilidis, A. ; Drusvyatskiy, D. ; Lewis, A. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c292t-cc0afe18418515b136fd11236c31187e7ac671aec1aaa36c39bf800a61bfbf4c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Eigenvalues</topic><topic>Euclidean space</topic><topic>Optimization algorithms</topic><topic>Values</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Daniilidis, A.</creatorcontrib><creatorcontrib>Drusvyatskiy, D.</creatorcontrib><creatorcontrib>Lewis, A. S.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>SIAM journal on matrix analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Daniilidis, A.</au><au>Drusvyatskiy, D.</au><au>Lewis, A. S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Orthogonal Invariance and Identifiability</atitle><jtitle>SIAM journal on matrix analysis and applications</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>35</volume><issue>2</issue><spage>580</spage><epage>598</epage><pages>580-598</pages><issn>0895-4798</issn><eissn>1095-7162</eissn><abstract>Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many active-set-type optimization algorithms. [PUBLICATION ABSTRACT]</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/130916710</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0895-4798 |
| ispartof | SIAM journal on matrix analysis and applications, 2014-01, Vol.35 (2), p.580-598 |
| issn | 0895-4798 1095-7162 |
| language | eng |
| recordid | cdi_proquest_journals_1524239069 |
| source | SIAM Journals |
| subjects | Eigenvalues Euclidean space Optimization algorithms Values |
| title | Orthogonal Invariance and Identifiability |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T04%3A53%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Orthogonal%20Invariance%20and%20Identifiability&rft.jtitle=SIAM%20journal%20on%20matrix%20analysis%20and%20applications&rft.au=Daniilidis,%20A.&rft.date=2014-01-01&rft.volume=35&rft.issue=2&rft.spage=580&rft.epage=598&rft.pages=580-598&rft.issn=0895-4798&rft.eissn=1095-7162&rft_id=info:doi/10.1137/130916710&rft_dat=%3Cproquest_cross%3E3302648931%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1524239069&rft_id=info:pmid/&rfr_iscdi=true |