{"id":"https://openalex.org/W7222939043","doi":"https://doi.org/10.48550/arxiv.2610.23206","title":"Synthesis of the Transient Behaviour of Optimization Algorithms for Strongly Convex Objective Functions","display_name":"Synthesis of the Transient Behaviour of Optimization Algorithms for Strongly Convex Objective Functions","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222939043","doi":"https://doi.org/10.48550/arxiv.2610.23206"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23206","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23206","pdf_url":"https://arxiv.org/pdf/2610.23206","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.23206","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093006906","display_name":"Adel Abdelsamed","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Abdelsamed, Adel","raw_affiliation_strings":["Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020972761","display_name":"Dennis Gramlich","orcid":"https://orcid.org/0000-0001-9188-9527","observed_orcids":["https://orcid.org/0000-0001-9188-9527"]},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gramlich, Dennis","raw_affiliation_strings":["Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany","Chair of Mathematical Systems Theory , University of Stuttgart , 70569 Stuttgart , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Chair of Mathematical Systems Theory , University of Stuttgart , 70569 Stuttgart , Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062156162","display_name":"Christian Ebenbauer","orcid":"https://orcid.org/0000-0002-7414-4299","observed_orcids":["https://orcid.org/0000-0002-7414-4299"]},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ebenbauer, Christian","raw_affiliation_strings":["Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035889063","display_name":"Carsten W. Scherer","orcid":"https://orcid.org/0000-0001-8856-2697","observed_orcids":["https://orcid.org/0000-0001-8856-2697"]},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Scherer, Carsten W.","raw_affiliation_strings":["Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.4629000127315521,"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":0.4629000127315521,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.2054000049829483,"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"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.14339999854564667,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transient-response","display_name":"transient response","score":0.8640000224113464},{"id":"https://openalex.org/keywords/first-order-methods","display_name":"first-order methods","score":0.8809999823570251},{"id":"https://openalex.org/keywords/strongly-convex-functions","display_name":"strongly convex functions","score":0.8980000019073486},{"id":"https://openalex.org/keywords/unconstrained-optimization","display_name":"unconstrained optimization","score":0.7120000123977661},{"id":"https://openalex.org/keywords/robust-h2-control","display_name":"robust H2 control","score":0.9700000286102295},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.9020000100135803},{"id":"https://openalex.org/keywords/worst-case-bounds","display_name":"worst-case bounds","score":0.6620000004768372},{"id":"https://openalex.org/keywords/feedback-delay","display_name":"feedback delay","score":0.6809999942779541}],"concepts":[{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.6574000120162964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6105999946594238},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5591999888420105},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5479999780654907},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.5282999873161316},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.522599995136261},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41920000314712524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41780000925064087},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.3995000123977661},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.3781999945640564},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.37630000710487366},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.36309999227523804},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.3596000075340271},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.32409998774528503},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32170000672340393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30390000343322754},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C85761212","wikidata":"https://www.wikidata.org/wiki/Q1974593","display_name":"Transient response","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29190000891685486},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.29100000858306885},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23206","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23206","pdf_url":"https://arxiv.org/pdf/2610.23206","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.23206","doi":"https://doi.org/10.48550/arxiv.2610.23206","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23206","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.23206","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23206","pdf_url":"https://arxiv.org/pdf/2610.23206","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222939043.pdf","grobid_xml":"https://content.openalex.org/works/W7222939043.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1962121538","https://openalex.org/W1979896658","https://openalex.org/W3123616448","https://openalex.org/W3158960540","https://openalex.org/W4388917752"],"related_works":["https://openalex.org/W3132336029","https://openalex.org/W2939326139","https://openalex.org/W4391020110","https://openalex.org/W3045583138","https://openalex.org/W4416659276","https://openalex.org/W7154275289","https://openalex.org/W7123354256","https://openalex.org/W7096059640","https://openalex.org/W2892538949","https://openalex.org/W2943533602"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,33,38,64,68,72,87],"transient":[3,111],"behavior":[4],"of":[5,12,99,116],"first-order":[6],"optimization":[7],"methods":[8,20],"for":[9,81],"unconstrained":[10],"minimization":[11],"smooth":[13],"and":[14,91,114],"strongly":[15],"convex":[16,56,78],"objective":[17],"functions.":[18],"These":[19],"are":[21],"modelled":[22],"as":[23],"linear":[24],"systems":[25],"over":[26,95],"finite-time":[27],"intervals":[28],"embedded":[29],"in":[30],"feedback":[31,120],"with":[32],"gradient":[34,107],"nonlinearity.":[35],"By":[36],"characterizing":[37],"function":[39],"class":[40],"through":[41],"discrete-time":[42],"Zames-Falb":[43],"integral":[44],"quadratic":[45],"constraints,":[46],"we":[47,75],"employ":[48],"a":[49,77,82],"robust":[50],"$\\mathcal{H}_2$":[51],"control":[52],"framework":[53,102],"to":[54,67,105],"obtain":[55],"semidefinite":[57],"programs":[58],"certifying":[59],"tight":[60],"worst-case":[61],"bounds":[62,90],"on":[63,71],"terminal":[65],"distance":[66],"optimizer.":[69],"Building":[70],"same":[73],"formulation,":[74],"derive":[76],"synthesis":[79,115],"procedure":[80],"transient-optimal":[83],"method":[84],"that":[85],"achieves":[86],"optimal":[88,117],"finite-horizon":[89],"guarantees":[92],"error":[93],"reduction":[94],"any":[96],"prescribed":[97],"number":[98],"steps.":[100],"The":[101],"naturally":[103],"extends":[104],"delayed":[106],"measurements,":[108],"enabling":[109],"both":[110],"performance":[112],"analysis":[113],"algorithms":[118],"under":[119],"delays.":[121]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-20T00:00:00"}