{"id":"https://openalex.org/W6887856361","doi":"https://doi.org/10.17615/b9hm-z330","title":"PREPROCESSING AND FIRST-ORDER PRIMAL-DUAL ALGORITHMS FOR CONVEX OPTIMIZATION","display_name":"PREPROCESSING AND FIRST-ORDER PRIMAL-DUAL ALGORITHMS FOR CONVEX OPTIMIZATION","publication_year":2021,"publication_date":"2021-02-04","ids":{"openalex":"https://openalex.org/W6887856361","doi":"https://doi.org/10.17615/b9hm-z330"},"language":"en","primary_location":{"id":"doi:10.17615/b9hm-z330","is_oa":true,"landing_page_url":"https://doi.org/10.17615/b9hm-z330","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"thesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.17615/b9hm-z330","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhu, Yuzixuan","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhu, Yuzixuan","raw_affiliation_strings":["University of North Carolina at Chapel Hill"],"affiliations":[{"raw_affiliation_string":"University of North Carolina at Chapel Hill","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I114027177"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26401379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7077000141143799,"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":0.7077000141143799,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.11670000106096268,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.07859999686479568,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.4514999985694885},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.39629998803138733},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.39079999923706055},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.3799999952316284},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.3504999876022339},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.3463999927043915},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.32670000195503235},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3188000023365021},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.30640000104904175}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6254000067710876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45910000801086426},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4115999937057495},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.39079999923706055},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3840000033378601},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3799999952316284},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3463999927043915},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.3052999973297119},{"id":"https://openalex.org/C62114133","wikidata":"https://www.wikidata.org/wiki/Q5366944","display_name":"L-reduction","level":5,"score":0.30219998955726624},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.2906000018119812},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.2533999979496002}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.17615/b9hm-z330","is_oa":true,"landing_page_url":"https://doi.org/10.17615/b9hm-z330","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"thesis"}],"best_oa_location":{"id":"doi:10.17615/b9hm-z330","is_oa":true,"landing_page_url":"https://doi.org/10.17615/b9hm-z330","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"thesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,196],"thesis":[1],"focuses":[2],"on":[3,79,110,173,188,193,202,246],"two":[4,130],"topics":[5],"in":[6,96,102,177],"the":[7,28,47,50,65,68,83,115,125,152,174,189,194],"field":[8],"of":[9,31,49,55,67,100,138,151],"convex":[10,238],"optimization:":[11],"preprocessing":[12],"algorithms":[13,21,133,157,245,258],"for":[14,22],"semidefinite":[15],"programs":[16],"(SDPs),":[17],"and":[18,61,63,160,182,191,252],"first-order":[19,131],"primal-dual":[20,132],"convex-concave":[23,139],"saddle-":[24],"point":[25],"problems.":[26,241],"In":[27,124],"first":[29,166],"part":[30],"this":[32],"thesis,":[33],"we":[34,128],"introduce":[35],"Sieve-SDP,":[36],"a":[37,97,136,208],"simple":[38],"facial":[39],"reduction":[40],"algorithm":[41,167,219],"to":[42,52,134,225,235,255],"preprocess":[43],"SDPs.":[44],"Sieve-SDP":[45],"inspects":[46],"constraints":[48],"problem":[51,112],"detect":[53],"lack":[54],"strict":[56],"feasibility,":[57],"deletes":[58],"redundant":[59],"rows":[60],"columns,":[62],"reduces":[64],"size":[66],"variable":[69],"matrix.":[70],"It":[71,75],"often":[72],"detects":[73],"infeasibility.":[74],"does":[76],"not":[77],"rely":[78],"any":[80],"optimization":[81],"solver:":[82],"only":[84],"subroutine":[85],"it":[86,92],"needs":[87],"is":[88],"Cholesky":[89],"factorization,":[90],"hence":[91],"can":[93,168,198,220,232],"be":[94,199,233],"implemented":[95],"few":[98],"lines":[99],"code":[101],"machine":[103],"precision.":[104],"We":[105,242],"present":[106],"extensive":[107],"computational":[108],"results":[109,231],"several":[111],"collections":[113],"from":[114,121],"literature,":[116],"with":[117,259],"many":[118,153],"SDPs":[119],"coming":[120],"polynomial":[122],"optimization.":[123],"second":[126,218],"part,":[127],"develop":[129],"solve":[135],"class":[137],"saddle-point":[140],"problems":[141],"involving":[142],"non-bilinear":[143],"coupling":[144],"function,":[145],"which":[146],"includes":[147],"SDP":[148],"as":[149,249],"one":[150],"special":[154],"cases.":[155],"Both":[156],"are":[158],"single-loop":[159],"have":[161],"low":[162],"per-iteration":[163],"complexity.":[164],"Our":[165,230],"achieve":[169],"O(1/k)":[170],"convergence":[171,223],"rates":[172,224],"duality":[175],"gap":[176],"both":[178],"ergodic":[179,192],"(averaging)":[180],"sense":[181],"semi-ergodic":[183],"sense,":[184],"i.e.,":[185],"non-ergodic":[186,203],"(last-iterate)":[187],"primal,":[190],"dual.":[195],"rate":[197],"further":[200],"improved":[201],"primal":[204],"objective":[205],"residual":[206],"using":[207],"new":[209],"parameter":[210],"update":[211],"rule.":[212],"Under":[213],"strong":[214],"convexity":[215],"assumption,":[216],"our":[217,244,257],"boost":[221],"these":[222],"no":[226],"slower":[227],"than":[228],"O(1/k^2).":[229],"specified":[234],"handle":[236],"general":[237],"cone":[239],"constrained":[240],"test":[243],"applications":[247],"such":[248],"two-player":[250],"games":[251],"image":[253],"processing":[254],"compare":[256],"existing":[260],"methods.":[261]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}