{"id":"https://openalex.org/W7160526545","doi":"https://doi.org/10.1007/s10957-026-02999-z","title":"Convergent Lifted Lasserre Hierarchy of SDPs for Minimizing Expectation of Piecewise Polynomial Loss over Wasserstein Balls","display_name":"Convergent Lifted Lasserre Hierarchy of SDPs for Minimizing Expectation of Piecewise Polynomial Loss over Wasserstein Balls","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W7160526545","doi":"https://doi.org/10.1007/s10957-026-02999-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-02999-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-026-02999-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-026-02999-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/s10957-026-02999-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135577149","display_name":"Neil De Vera Dizon","orcid":"https://orcid.org/0000-0001-8664-2255"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Neil De Vera Dizon","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":"https://orcid.org/0000-0001-8664-2255","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101524587","display_name":"Queenie Yingkun Huang","orcid":"https://orcid.org/0009-0003-3994-5941"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Queenie Yingkun Huang","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024668916","display_name":"Th\u00e1i Do\u00e3n Ch\u01b0\u01a1ng","orcid":"https://orcid.org/0000-0003-0893-5604"},"institutions":[{"id":"https://openalex.org/I59433898","display_name":"Brunel University of London","ror":"https://ror.org/00dn4t376","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I59433898"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thai Doan Chuong","raw_affiliation_strings":["Department of Mathematics, Brunel University London, London, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Brunel University London, London, England","institution_ids":["https://openalex.org/I59433898"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135555034","display_name":"Guoyin Li","orcid":null},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guoyin Li","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026027785","display_name":"V. Jeyakumar","orcid":"https://orcid.org/0000-0003-0267-7800"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Vaithilingam Jeyakumar","raw_affiliation_strings":["Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5135577149"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.67041228,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"209","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.7674999833106995,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.7674999833106995,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.07339999824762344,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.05889999866485596,"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/piecewise","display_name":"Piecewise","score":0.7246999740600586},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6646999716758728},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6043999791145325},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.555400013923645},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4300999939441681},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.400299996137619}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.847599983215332},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7246999740600586},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6646999716758728},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6043999791145325},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5199999809265137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4740999937057495},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C2780394207","wikidata":"https://www.wikidata.org/wiki/Q7449304","display_name":"Semi-infinite programming","level":3,"score":0.274399995803833},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-026-02999-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-026-02999-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-026-02999-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:bura.brunel.ac.uk:2438/33442","is_oa":true,"landing_page_url":"https://bura.brunel.ac.uk/handle/2438/33442","pdf_url":null,"source":{"id":"https://openalex.org/S4306401473","display_name":"Brunel University Research Archive (BURA) (Brunel University London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59433898","host_organization_name":"Brunel University of London","host_organization_lineage":["https://openalex.org/I59433898"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10957-026-02999-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-026-02999-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-026-02999-z.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44914382696151733,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7160526545.pdf","grobid_xml":"https://content.openalex.org/works/W7160526545.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W214108230","https://openalex.org/W404764422","https://openalex.org/W622935592","https://openalex.org/W1559197676","https://openalex.org/W1647779468","https://openalex.org/W1968355947","https://openalex.org/W1970515840","https://openalex.org/W1970699014","https://openalex.org/W1974962384","https://openalex.org/W2001334051","https://openalex.org/W2009348384","https://openalex.org/W2016403269","https://openalex.org/W2069764498","https://openalex.org/W2083247753","https://openalex.org/W2114605231","https://openalex.org/W2125417745","https://openalex.org/W2129353652","https://openalex.org/W2140748229","https://openalex.org/W2150111299","https://openalex.org/W2153473676","https://openalex.org/W2255400221","https://openalex.org/W2327195030","https://openalex.org/W2336156739","https://openalex.org/W2593062745","https://openalex.org/W2779887607","https://openalex.org/W2963450292","https://openalex.org/W2964239200","https://openalex.org/W2969738732","https://openalex.org/W2972299727","https://openalex.org/W2972919843","https://openalex.org/W2975012327","https://openalex.org/W3031808047","https://openalex.org/W3123325486","https://openalex.org/W3124187518","https://openalex.org/W3176590421","https://openalex.org/W4251616545","https://openalex.org/W4255442211","https://openalex.org/W4311064410","https://openalex.org/W4382323324","https://openalex.org/W4391800739","https://openalex.org/W4410279011","https://openalex.org/W4411917733"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1,17],"paper":[2],"investigates":[3],"the":[4,7,33,49,63,94,104],"minimization":[5],"of":[6,9,26,36,39,52,65,86,114],"expectation":[8],"piecewise":[10,74],"polynomial":[11],"loss":[12],"functions":[13],"over":[14,77],"Wasserstein":[15],"balls.":[16],"optimization":[18,29,56],"problem":[19],"often":[20],"appears":[21],"as":[22],"a":[23,37,45,66,83],"key":[24],"sub-problem":[25],"distributionally":[27],"robust":[28],"problems.":[30,57],"We":[31],"establish":[32],"asymptotic":[34],"convergence":[35,99],"hierarchy":[38,96],"semi-definite":[40],"programming":[41],"(SDP)":[42],"relaxations,":[43],"providing":[44],"framework":[46],"for":[47],"approximating":[48],"optimal":[50],"values":[51],"these":[53],"inherently":[54],"infinite-dimensional":[55],"A":[58],"central":[59],"foundational":[60],"contribution":[61],"is":[62],"development":[64],"new":[67],"lifted":[68],"positivity":[69],"certificate:":[70],"we":[71,91],"demonstrate":[72],"that":[73,93],"polynomials":[75,106],"positive":[76],"Archimedean":[78],"basic":[79],"semi-algebraic":[80],"sets":[81],"admit":[82],"structured":[84],"system":[85],"sum-of-squares":[87],"(SOS)":[88],"representations.":[89],"Furthermore,":[90],"prove":[92],"proposed":[95],"achieves":[97],"finite":[98],"under":[100],"suitable":[101],"conditions":[102],"when":[103],"defining":[105],"are":[107,117],"convex.":[108],"The":[109],"practical":[110],"utility":[111],"and":[112,125],"versatility":[113],"this":[115],"approach":[116],"demonstrated":[118],"via":[119],"numerical":[120],"experiments":[121],"in":[122],"revenue":[123],"estimation":[124],"portfolio":[126],"optimization.":[127]},"counts_by_year":[],"updated_date":"2026-06-20T20:08:15.867695","created_date":"2026-05-08T00:00:00"}
