{"id":"https://openalex.org/W2064735708","doi":"https://doi.org/10.1007/s10107-012-0612-1","title":"MM algorithms for geometric and signomial programming","display_name":"MM algorithms for geometric and signomial programming","publication_year":2012,"publication_date":"2012-10-25","ids":{"openalex":"https://openalex.org/W2064735708","doi":"https://doi.org/10.1007/s10107-012-0612-1","mag":"2064735708","pmid":"https://pubmed.ncbi.nlm.nih.gov/24634545"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-012-0612-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-012-0612-1","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1007.2371","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kenneth Lange","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth Lange","raw_affiliation_strings":["Departments of Biomathematics, Human Genetics, and Statistics, University of California, Los Angeles, CA 90095-1766, USA. klange@ucla.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Biomathematics, Human Genetics, and Statistics, University of California, Los Angeles, CA 90095-1766, USA. klange@ucla.edu","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hua Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hua Zhou","raw_affiliation_strings":["Department of Statistics, North Carolina State University, 2311 Stinson Drive, Campus Box 8203, Raleigh, NC 27695-8203, USA. hua_zhou@ncsu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, North Carolina State University, 2311 Stinson Drive, Campus Box 8203, Raleigh, NC 27695-8203, USA. hua_zhou@ncsu.edu","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":4.0955,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.93930348,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"143","issue":"1-2","first_page":"339","last_page":"356"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.8848999738693237,"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":0.8848999738693237,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.08699999749660492,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/hyperplane","display_name":"Hyperplane","score":0.7418000102043152},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.49950000643730164},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4912000000476837},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47699999809265137},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.47540000081062317},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4674000144004822},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.4616999924182892},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.446399986743927},{"id":"https://openalex.org/keywords/geometric-programming","display_name":"Geometric programming","score":0.4352000057697296}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8611000180244446},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7418000102043152},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5382999777793884},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49950000643730164},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4912000000476837},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.486299991607666},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47699999809265137},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.47540000081062317},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4674000144004822},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.4616999924182892},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.38280001282691956},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C2778712213","wikidata":"https://www.wikidata.org/wiki/Q20740046","display_name":"Calmness","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C86941820","wikidata":"https://www.wikidata.org/wiki/Q6865391","display_name":"Minimisation (clinical trials)","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2563000023365021},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2547999918460846}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10107-012-0612-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-012-0612-1","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmid:24634545","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24634545","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical programming","raw_type":null},{"id":"pmh:oai:arXiv.org:1007.2371","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1007.2371","pdf_url":"https://arxiv.org/pdf/1007.2371","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:3950732","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3950732","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Math Program","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1007.2371","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1007.2371","pdf_url":"https://arxiv.org/pdf/1007.2371","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2048638135","display_name":null,"funder_award_id":"R01 MH059490","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"},{"id":"https://openalex.org/G6465883393","display_name":null,"funder_award_id":"MH59490","funder_id":"https://openalex.org/F4320332505","funder_display_name":"U.S. Public Health Service"},{"id":"https://openalex.org/G7974732270","display_name":null,"funder_award_id":"R37 MH059490","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"},{"id":"https://openalex.org/G8009928313","display_name":null,"funder_award_id":"R01 GM053275","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G8583520036","display_name":null,"funder_award_id":"GM53275","funder_id":"https://openalex.org/F4320332505","funder_display_name":"U.S. Public Health Service"},{"id":"https://openalex.org/G950618099","display_name":null,"funder_award_id":"R01 HG006139","funder_id":"https://openalex.org/F4320337348","funder_display_name":"National Human Genome Research Institute"}],"funders":[{"id":"https://openalex.org/F4320332505","display_name":"U.S. Public Health Service","ror":"https://ror.org/05xf94514"},{"id":"https://openalex.org/F4320337346","display_name":"National Institute of Mental Health","ror":"https://ror.org/04xeg9z08"},{"id":"https://openalex.org/F4320337348","display_name":"National Human Genome Research Institute","ror":"https://ror.org/00baak391"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2064735708.pdf","grobid_xml":"https://content.openalex.org/works/W2064735708.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1278605765","https://openalex.org/W1971781586","https://openalex.org/W1986333823","https://openalex.org/W1992651809","https://openalex.org/W2025733515","https://openalex.org/W2039284087","https://openalex.org/W2074899312","https://openalex.org/W2076007362","https://openalex.org/W2083501069","https://openalex.org/W2094302545","https://openalex.org/W2106476087","https://openalex.org/W2149232990","https://openalex.org/W2149414429","https://openalex.org/W2165239860","https://openalex.org/W2171048418","https://openalex.org/W4248341828","https://openalex.org/W4250589301","https://openalex.org/W4255600897","https://openalex.org/W4293775970","https://openalex.org/W4302155765","https://openalex.org/W6600005384"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}