{"id":"https://openalex.org/W2893172655","doi":"https://doi.org/10.1137/18m1215682","title":"Hessian Barrier Algorithms for Linearly Constrained Optimization Problems","display_name":"Hessian Barrier Algorithms for Linearly Constrained Optimization Problems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2893172655","doi":"https://doi.org/10.1137/18m1215682","mag":"2893172655"},"language":"en","primary_location":{"id":"doi:10.1137/18m1215682","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1215682","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1809.09449","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023776719","display_name":"Immanuel M. Bomze","orcid":"https://orcid.org/0000-0002-6288-9226"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Immanuel M. Bomze","raw_affiliation_strings":["Univ of Vienna"],"affiliations":[{"raw_affiliation_string":"Univ of Vienna","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018966648","display_name":"Panayotis Mertikopoulos","orcid":"https://orcid.org/0000-0003-2026-9616"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panayotis Mertikopoulos","raw_affiliation_strings":["CNRS"],"affiliations":[{"raw_affiliation_string":"CNRS","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021031996","display_name":"Werner Schachinger","orcid":"https://orcid.org/0000-0003-0778-4074"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Werner Schachinger","raw_affiliation_strings":["Univ of Vienna"],"affiliations":[{"raw_affiliation_string":"Univ of Vienna","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091142361","display_name":"Mathias Staudigl","orcid":"https://orcid.org/0000-0003-2481-0019"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mathias Staudigl","raw_affiliation_strings":["QE / Econometrics"],"affiliations":[{"raw_affiliation_string":"QE / Econometrics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023776719"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00569147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"3","first_page":"2100","last_page":"2127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7425041198730469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.720672070980072},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5725803971290588},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.4706741273403168},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.46144169569015503},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45756796002388},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4523344039916992},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.45106014609336853},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4486793875694275},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.43697795271873474},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.4256751835346222},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.411435067653656},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.3213535249233246},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3083730936050415},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.28308701515197754},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.25973543524742126},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.19126099348068237},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19056978821754456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16165998578071594},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14488574862480164},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08241438865661621}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7425041198730469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.720672070980072},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5725803971290588},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.4706741273403168},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.46144169569015503},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45756796002388},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4523344039916992},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.45106014609336853},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4486793875694275},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.43697795271873474},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.4256751835346222},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.411435067653656},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3213535249233246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3083730936050415},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.28308701515197754},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25973543524742126},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.19126099348068237},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19056978821754456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16165998578071594},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14488574862480164},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08241438865661621},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1137/18m1215682","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1215682","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.09449","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.09449","pdf_url":"https://arxiv.org/pdf/1809.09449","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:cris.maastrichtuniversity.nl:publications/c9854bf2-1c1a-43b9-b377-945f2975b10f","is_oa":true,"landing_page_url":"https://cris.maastrichtuniversity.nl/en/publications/c9854bf2-1c1a-43b9-b377-945f2975b10f","pdf_url":"https://cris.maastrichtuniversity.nl/en/publications/c9854bf2-1c1a-43b9-b377-945f2975b10f","source":{"id":"https://openalex.org/S4306402616","display_name":"Research Publications (Maastricht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I34352273","host_organization_name":"Maastricht University","host_organization_lineage":["https://openalex.org/I34352273"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bomze, I M, Mertikopoulos, P, Schachinger, W & Staudigl, M 2019, 'Hessian barrier algorithms for linearly constrained optimization problems', Siam Journal on Optimization, vol. 29, no. 3, pp. 2100-2127. https://doi.org/10.1137/18M1215682","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"mag:2893172655","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1809.09449","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01891539v1","is_oa":false,"landing_page_url":"https://hal.inria.fr/hal-01891539","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/hal-01891539","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-02403531v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02403531","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2019, 29, pp.2100 - 2127. ⟨10.1137/18M1215682⟩","raw_type":"Journal articles"},{"id":"pmh:oai:cris.maastrichtuniversity.nl:openaire_cris_publications/dbc9724a-6a3f-4cad-b073-2ec04d488f79","is_oa":true,"landing_page_url":"https://cris.maastrichtuniversity.nl/en/publications/dbc9724a-6a3f-4cad-b073-2ec04d488f79","pdf_url":null,"source":{"id":"https://openalex.org/S4306402616","display_name":"Research Publications (Maastricht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I34352273","host_organization_name":"Maastricht University","host_organization_lineage":["https://openalex.org/I34352273"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bomze , I , Mertikopoulos , P , Schachinger , W & Staudigl , M 2018 ' Hessian barrier algorithms for linearly constrained optimization problems ' Cornell University - arXiv . https://doi.org/10.48550/arXiv.1809.09449","raw_type":"workingPaper"},{"id":"pmh:oai:ub-madoc.bib.uni-mannheim.de:64986","is_oa":false,"landing_page_url":"https://madoc.bib.uni-mannheim.de/64986/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196315","display_name":"MADOC (University of Mannheim)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177802217","host_organization_name":"University of Mannheim","host_organization_lineage":["https://openalex.org/I177802217"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Zeitschriftenartikel"},{"id":"doi:10.48550/arxiv.1809.09449","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.09449","pdf_url":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1809.09449","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.09449","pdf_url":"https://arxiv.org/pdf/1809.09449","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6109462662","display_name":null,"funder_award_id":"ANR-16-CE33-0004-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8301030878","display_name":null,"funder_award_id":"&quot","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8923725977","display_name":"Online resource allocation for unpredictable large-scale wireless systems","funder_award_id":"ANR-16-CE33-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1546734293","https://openalex.org/W1550538040","https://openalex.org/W1837565340","https://openalex.org/W1967138577","https://openalex.org/W1967862529","https://openalex.org/W1970033879","https://openalex.org/W1970911233","https://openalex.org/W1979207064","https://openalex.org/W1986891697","https://openalex.org/W1987083649","https://openalex.org/W1987161519","https://openalex.org/W1989166601","https://openalex.org/W2004742270","https://openalex.org/W2016384870","https://openalex.org/W2018478336","https://openalex.org/W2018556306","https://openalex.org/W2027574304","https://openalex.org/W2029465407","https://openalex.org/W2031623512","https://openalex.org/W2034260606","https://openalex.org/W2036083037","https://openalex.org/W2045867632","https://openalex.org/W2055954415","https://openalex.org/W2067952903","https://openalex.org/W2079576032","https://openalex.org/W2086920040","https://openalex.org/W2100556411","https://openalex.org/W2113416387","https://openalex.org/W2129131372","https://openalex.org/W2156374634","https://openalex.org/W2169713291","https://openalex.org/W2409973437","https://openalex.org/W2528062157","https://openalex.org/W2551645646","https://openalex.org/W2587436146","https://openalex.org/W2762341112","https://openalex.org/W2783096200","https://openalex.org/W2962676888","https://openalex.org/W2963430672","https://openalex.org/W4206742934","https://openalex.org/W4251295118","https://openalex.org/W4292022450"],"related_works":["https://openalex.org/W3034209907","https://openalex.org/W1993553082","https://openalex.org/W1971926417","https://openalex.org/W2951926417","https://openalex.org/W3125780245","https://openalex.org/W2949205556","https://openalex.org/W1989412488","https://openalex.org/W2984687545","https://openalex.org/W2227972400","https://openalex.org/W2742599086","https://openalex.org/W3118483319","https://openalex.org/W3151606440","https://openalex.org/W3170531556","https://openalex.org/W3010123052","https://openalex.org/W2198183204","https://openalex.org/W2944447206","https://openalex.org/W2966160890","https://openalex.org/W2963648037","https://openalex.org/W2775790982","https://openalex.org/W3105393233"],"abstract_inverted_index":{"In":[0,37,99],"this":[1,38],"paper,":[2],"we":[3,16,110],"propose":[4],"an":[5,32,45],"interior-point":[6],"method":[7],"for":[8,120],"linearly":[9,103],"constrained---and":[10],"possibly":[11],"nonconvex---optimization":[12],"problems.":[13,155],"The":[14],"method---which":[15],"call":[17],"the":[18,55,77,81,87,90,95,100,114,127,135],"Hessian":[19],"barrier":[20],"algorithm":[21,78,91],"(HBA)---combines":[22],"a":[23,74],"forward":[24],"Euler":[25],"discretization":[26],"of":[27,102,129],"Hessian--Riemannian":[28],"gradient":[29],"flows":[30],"with":[31],"Armijo":[33],"backtracking":[34],"step-size":[35],"policy.":[36],"way,":[39],"HBA":[40],"can":[41],"be":[42],"seen":[43],"as":[44,52],"alternative":[46],"to":[47,80,94],"mirror":[48],"descent,":[49],"and":[50,62,151],"contains":[51],"special":[53],"cases":[54],"affine":[56],"scaling":[57],"algorithm,":[58],"regularized":[59],"Newton":[60],"processes,":[61],"several":[63],"other":[64],"iterative":[65],"solution":[66],"methods.":[67],"Our":[68],"main":[69],"result":[70],"is":[71,118],"that,":[72],"modulo":[73],"nondegeneracy":[75],"condition,":[76],"converges":[79,92],"problem's":[82,96,136],"critical":[83],"set;":[84],"hence,":[85],"in":[86,146],"convex":[88],"case,":[89],"globally":[93],"minimum":[97],"set.":[98],"case":[101],"constrained":[104],"quadratic":[105],"programs":[106],"(not":[107],"necessarily":[108],"convex),":[109],"also":[111],"show":[112],"that":[113,123],"method's":[115],"convergence":[116],"rate":[117],"$O(1/k\\rho)$":[119],"some":[121],"$\\rho\\in(0,1]$":[122],"depends":[124],"only":[125],"on":[126,134],"choice":[128],"kernel":[130],"function":[131],"(i.e.,":[132],"not":[133],"primitives).":[137],"These":[138],"theoretical":[139],"results":[140],"are":[141],"validated":[142],"by":[143],"numerical":[144],"experiments":[145],"standard":[147],"nonconvex":[148],"test":[149],"functions":[150],"large-scale":[152],"traffic":[153],"assignment":[154]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}