{"id":"https://openalex.org/W4414207205","doi":"https://doi.org/10.1007/s12532-025-00290-2","title":"Improving the solution of indefinite quadratic programs and linear programs with complementarity constraints by a progressive MIP method","display_name":"Improving the solution of indefinite quadratic programs and linear programs with complementarity constraints by a progressive MIP method","publication_year":2025,"publication_date":"2025-09-16","ids":{"openalex":"https://openalex.org/W4414207205","doi":"https://doi.org/10.1007/s12532-025-00290-2"},"language":"en","primary_location":{"id":"doi:10.1007/s12532-025-00290-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00290-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00290-2.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00290-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058902890","display_name":"Xinyao Zhang","orcid":"https://orcid.org/0000-0003-3850-678X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xinyao Zhang","raw_affiliation_strings":["The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, 90066, USA"],"affiliations":[{"raw_affiliation_string":"The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, 90066, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090956170","display_name":"Shaoning Han","orcid":"https://orcid.org/0000-0003-1145-7981"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Shaoning Han","raw_affiliation_strings":["Department of Mathematics, Institute of Operations Research and Analytics, National University of Singapore, Singapore, 119076, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Institute of Operations Research and Analytics, National University of Singapore, Singapore, 119076, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002789695","display_name":"Jong\u2010Shi Pang","orcid":"https://orcid.org/0000-0002-2224-6787"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jong-Shi Pang","raw_affiliation_strings":["The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, 90066, USA"],"affiliations":[{"raw_affiliation_string":"The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, 90066, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058902890"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":{"value":2390,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2390,"currency":"EUR","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37067076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"135","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9975000023841858,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965999722480774,"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/theory-of-computation","display_name":"Theory of computation","score":0.6669999957084656},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.621399998664856},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.5626999735832214},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.553600013256073},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5248000025749207},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4828000068664551},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4742000102996826},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4659999907016754}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6669999957084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.659500002861023},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6459000110626221},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.621399998664856},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.5626999735832214},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.553600013256073},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5248000025749207},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4659999907016754},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.412200003862381},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.3928999900817871},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.3750999867916107},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3319000005722046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.328900009393692},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.3278000056743622},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32019999623298645},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.29919999837875366},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2623000144958496}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12532-025-00290-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00290-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00290-2.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12532-025-00290-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12532-025-00290-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12532-025-00290-2.pdf","source":{"id":"https://openalex.org/S173077093","display_name":"Mathematical Programming Computation","issn_l":"1867-2949","issn":["1867-2949","1867-2957"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1482925484","display_name":null,"funder_award_id":"Tier 1","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G416181279","display_name":null,"funder_award_id":"Academic Research Fund Tier 1","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G5016601650","display_name":null,"funder_award_id":"Academic Research Fund","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G8363208187","display_name":null,"funder_award_id":"FY2024","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G901625343","display_name":null,"funder_award_id":"Academic Research F","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414207205.pdf","grobid_xml":"https://content.openalex.org/works/W4414207205.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W180478659","https://openalex.org/W1481481825","https://openalex.org/W1503085769","https://openalex.org/W1512031962","https://openalex.org/W1518832340","https://openalex.org/W1543439990","https://openalex.org/W1579101628","https://openalex.org/W1720757687","https://openalex.org/W1870318758","https://openalex.org/W1966081460","https://openalex.org/W1971536112","https://openalex.org/W1971700807","https://openalex.org/W1972243042","https://openalex.org/W1973799058","https://openalex.org/W2000151369","https://openalex.org/W2000923338","https://openalex.org/W2012886081","https://openalex.org/W2016445775","https://openalex.org/W2018556306","https://openalex.org/W2020696014","https://openalex.org/W2021674665","https://openalex.org/W2027470314","https://openalex.org/W2028042462","https://openalex.org/W2031494345","https://openalex.org/W2034039293","https://openalex.org/W2048799772","https://openalex.org/W2063790063","https://openalex.org/W2068671103","https://openalex.org/W2079384027","https://openalex.org/W2091988699","https://openalex.org/W2092218813","https://openalex.org/W2106292145","https://openalex.org/W2123871098","https://openalex.org/W2131524354","https://openalex.org/W2139624848","https://openalex.org/W2607956614","https://openalex.org/W2962818638","https://openalex.org/W2963575397","https://openalex.org/W3022556914","https://openalex.org/W3045179171","https://openalex.org/W3121235808","https://openalex.org/W4231147659","https://openalex.org/W4411510972"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Indefinite":[1],"quadratic":[2],"programs":[3,20],"(QPs)":[4],"are":[5,18],"known":[6,206],"to":[7,11,14,60,62,262],"be":[8,12,202,263],"very":[9],"difficult":[10],"solved":[13],"global":[15],"optimality,":[16],"so":[17],"linear":[19,22,77],"with":[21,35,90,114,237],"complementarity":[23,99],"constraints":[24],"(LPCCs).":[25],"It":[26,176],"is":[27,58,177,191,221,259,273],"a":[28,33,46,68,73,82,91,105,115,192,198,224,232,250,266,277,303],"classic":[29],"result":[30],"that":[31,180,200,258,275],"for":[32,80,139,209],"QP":[34,40,66,304],"an":[36,42,64,148,254],"optimal":[37,54],"solution,":[38],"the":[39,88,98,101,128,154,158,162,166,170,181,185,188,196,216,218,228,245,281,284,289,293,300,315],"has":[41,309],"equivalent":[43],"formulation":[44,168,308],"as":[45,67],"certain":[47],"LPCC":[48,89,229,285,307],"in":[49,172,288,314],"terms":[50],"of":[51,86,94,108,118,151,157,165,169,187,195,227,253,280,283,292,299],"their":[52],"globally":[53],"solutions.":[55,175],"Thus":[56],"it":[57],"natural":[59],"attempt":[61],"solve":[63],"(indefinite)":[65],"LPCC.":[69,84],"This":[70,296],"paper":[71],"presents":[72],"progressive":[74,131,159],"mixed":[75,109],"integer":[76,95,110,119,132],"programming":[78,234,268],"method":[79,103,134,190,208,220,247],"solving":[81,87,210],"general":[83],"Instead":[85],"full":[92],"set":[93,150],"variables":[96,120],"expressing":[97],"conditions,":[100],"presented":[102,274],"solves":[104],"finite":[106],"number":[107],"subprograms":[111],"by":[112,204,265],"starting":[113],"small":[116],"fraction":[117],"and":[121,135,142,236,305],"progressively":[122],"increasing":[123],"this":[124,211],"fraction.":[125],"After":[126],"describing":[127],"PIP":[129,189,219,246],"(for":[130],"programming)":[133],"providing":[136],"some":[137,271],"details":[138],"its":[140,306],"implementation":[141],"tuning":[143],"possibilities,":[144],"we":[145],"demonstrate,":[146],"via":[147],"extensive":[149],"computational":[152],"experiments,":[153,217],"superior":[155],"performance":[156],"approach":[160],"over":[161],"direct":[163],"solution":[164,182,226,252],"full-integer":[167],"LPCCs":[171],"obtaining":[173],"high-quality":[174],"also":[178],"shown":[179],"obtained":[183,230],"at":[184,223],"termination":[186],"local":[193,290,297],"minimizer":[194],"LPCC,":[197],"property":[199],"cannot":[201],"claimed":[203],"any":[205],"non-enumerative":[207],"nonconvex":[212],"program.":[213],"In":[214],"all":[215],"initiated":[222],"feasible":[225],"from":[231],"nonlinear":[233,267],"solver,":[235],"high":[238],"likelihood,":[239],"can":[240,248],"successfully":[241],"improve":[242,249],"it.":[243],"Thus,":[244],"stationary":[251],"indefinite":[255,294],"QP,":[256],"something":[257],"not":[260,311],"likely":[261],"achievable":[264],"method.":[269],"Finally,":[270],"analysis":[272],"provides":[276],"better":[278],"understanding":[279],"roles":[282],"suboptimal":[286],"solutions":[287],"optimality":[291],"QP.":[295],"aspect":[298],"connection":[301],"between":[302],"seemingly":[310],"been":[312],"addressed":[313],"literature.":[316]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
