{"id":"https://openalex.org/W1527552358","doi":"https://doi.org/10.1007/3-540-59408-6_46","title":"Combining semidefinite and polyhedral relaxations for integer programs","display_name":"Combining semidefinite and polyhedral relaxations for integer programs","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1527552358","doi":"https://doi.org/10.1007/3-540-59408-6_46","mag":"1527552358"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-59408-6_46","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59408-6_46","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058749822","display_name":"Christoph Helmberg","orcid":"https://orcid.org/0000-0002-5288-8000"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"C. Helmberg","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Graz, Kopernikusgasse 24, A-8010, Graz, Austria","Technische Universit\u00c4t Graz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Graz, Kopernikusgasse 24, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Technische Universit\u00c4t Graz","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108447927","display_name":"S. Poljak","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. Poljak","raw_affiliation_strings":["Institut f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, Innstra\u00dfe 33, 94030, Passau, Germany","Universit\u00e4t Passau,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, Innstra\u00dfe 33, 94030, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"Universit\u00e4t Passau,","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036114620","display_name":"Franz Rendl","orcid":"https://orcid.org/0000-0003-1578-9414"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"F. Rendl","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Graz, Kopernikusgasse 24, A-8010, Graz, Austria","Technische Universit\u00c4t Graz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Graz, Kopernikusgasse 24, A-8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Technische Universit\u00c4t Graz","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061777786","display_name":"Henry Wolkowicz","orcid":"https://orcid.org/0000-0003-1572-3060"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"H. Wolkowicz","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada","(University of Waterloo)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":10.3409,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.98888889,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"124","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.9145172238349915},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.8509803414344788},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.7533589601516724},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6764928102493286},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.635023295879364},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.5741109848022461},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5632416605949402},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5325931906700134},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5099316835403442},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5003671646118164},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4841080904006958},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.44790762662887573},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4244280755519867},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.41869157552719116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37853896617889404},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22701901197433472}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.9145172238349915},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.8509803414344788},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.7533589601516724},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6764928102493286},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.635023295879364},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.5741109848022461},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5632416605949402},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5325931906700134},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5099316835403442},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5003671646118164},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4841080904006958},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.44790762662887573},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4244280755519867},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.41869157552719116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37853896617889404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22701901197433472},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-59408-6_46","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59408-6_46","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.2861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.2861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://orion.math.uwaterloo.ca/~hwolkowi/henry/reports/ipco.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1509288136","https://openalex.org/W1963753244","https://openalex.org/W1970193303","https://openalex.org/W2031978868","https://openalex.org/W2058497129","https://openalex.org/W2065141624","https://openalex.org/W2066492681","https://openalex.org/W2078289947","https://openalex.org/W2080905757","https://openalex.org/W2092812429","https://openalex.org/W2106264302","https://openalex.org/W2128202699","https://openalex.org/W2148016452","https://openalex.org/W2590349623","https://openalex.org/W2917997019","https://openalex.org/W6666762136"],"related_works":["https://openalex.org/W2348903644","https://openalex.org/W2975050997","https://openalex.org/W2737505353","https://openalex.org/W2912522929","https://openalex.org/W1653317167","https://openalex.org/W1989828432","https://openalex.org/W2364528045","https://openalex.org/W2352839224","https://openalex.org/W2385886188","https://openalex.org/W2461836650"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}