{"id":"https://openalex.org/W1487833069","doi":"https://doi.org/10.1109/cdc.2003.1271745","title":"Polynomial complexity for a Nesterov-Todd potential-reduction method with inexact search directions","display_name":"Polynomial complexity for a Nesterov-Todd potential-reduction method with inexact search directions","publication_year":2004,"publication_date":"2004-04-23","ids":{"openalex":"https://openalex.org/W1487833069","doi":"https://doi.org/10.1109/cdc.2003.1271745","mag":"1487833069"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2003.1271745","is_oa":false,"landing_page_url":"http://doi.org/10.1109/cdc.2003.1271745","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},"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/A5070712941","display_name":"Jonas Gillberg","orcid":null},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"J. Gillberg","raw_affiliation_strings":["[Dept. of Electr. Eng., Linkoping Univ., Sweden]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Dept. of Electr. Eng., Linkoping Univ., Sweden]","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113604613","display_name":"Anders Hansson","orcid":null},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"A. Hansson","raw_affiliation_strings":["[Dept. of Electr. Eng., Linkoping Univ., Sweden]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Dept. of Electr. Eng., Linkoping Univ., Sweden]","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I102134673"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3824","last_page":"3829"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/preconditioner","display_name":"Preconditioner","score":0.8148049116134644},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6693071722984314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6582950353622437},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6062883138656616},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5656459927558899},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5350568890571594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5250827074050903},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5192247033119202},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4632128179073334},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4440959692001343},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3115864098072052},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2903037369251251},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14644545316696167}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8148049116134644},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6693071722984314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6582950353622437},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6062883138656616},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5656459927558899},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5350568890571594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5250827074050903},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5192247033119202},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4632128179073334},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4440959692001343},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3115864098072052},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2903037369251251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14644545316696167},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2003.1271745","is_oa":false,"landing_page_url":"http://doi.org/10.1109/cdc.2003.1271745","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W572922989","https://openalex.org/W599826405","https://openalex.org/W1485217823","https://openalex.org/W1518039036","https://openalex.org/W2010315317","https://openalex.org/W2024457515","https://openalex.org/W2077418568","https://openalex.org/W2097944741","https://openalex.org/W2099139589","https://openalex.org/W2117065890","https://openalex.org/W2121762272","https://openalex.org/W2136801590","https://openalex.org/W2162681128","https://openalex.org/W2163630364","https://openalex.org/W2168204766","https://openalex.org/W2495457432","https://openalex.org/W2912522929","https://openalex.org/W4302564868","https://openalex.org/W6629010999","https://openalex.org/W6684293833"],"related_works":["https://openalex.org/W2159515580","https://openalex.org/W2081820376","https://openalex.org/W2277328098","https://openalex.org/W2091325992","https://openalex.org/W1964968800","https://openalex.org/W2059625160","https://openalex.org/W2006453807","https://openalex.org/W1987832651","https://openalex.org/W68723791","https://openalex.org/W2740546554"],"abstract_inverted_index":{"In":[0],"this":[1,57],"paper":[2],"is":[3,47],"discussed":[4],"how":[5],"to":[6,12,35],"efficiently":[7],"solve":[8],"semidefinite":[9],"programs":[10],"related":[11],"the":[13,36],"Kalman-Yakubovich-Popov":[14],"lemma.":[15],"We":[16,49],"consider":[17],"a":[18,30,51],"potential-reduction":[19],"method":[20,34],"where":[21],"Nesterov-Todd":[22],"search":[23],"directions":[24],"are":[25],"computed":[26],"inexactly":[27],"by":[28],"applying":[29],"preconditioned":[31],"conjugate":[32],"gradient":[33],"Schur":[37],"complement":[38],"equation.":[39],"An":[40],"efficient":[41],"preconditioner":[42],"based":[43],"on":[44],"Lyapunov":[45],"equations":[46],"derived.":[48],"give":[50],"proof":[52],"of":[53],"polynomial":[54],"convergence":[55],"for":[56],"interior":[58],"point":[59],"method.":[60]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
