{"id":"https://openalex.org/W4416064154","doi":"https://doi.org/10.48550/arxiv.2509.06833","title":"$\\ell_0$-Norm Multiobjective Optimization Models Motivated by Applications to Proton Therapy","display_name":"$\\ell_0$-Norm Multiobjective Optimization Models Motivated by Applications to Proton Therapy","publication_year":2025,"publication_date":"2025-09-08","ids":{"openalex":"https://openalex.org/W4416064154","doi":"https://doi.org/10.48550/arxiv.2509.06833"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.06833","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.06833","pdf_url":"https://arxiv.org/pdf/2509.06833","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.06833","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100584219","display_name":"Xiaoda Cong","orcid":"https://orcid.org/0009-0003-5175-630X","observed_orcids":["https://orcid.org/0009-0003-5175-630X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cong, Xiaoda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068845250","display_name":"Xuanfeng Ding","orcid":"https://orcid.org/0000-0002-1733-6278","observed_orcids":["https://orcid.org/0000-0002-1733-6278"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Xuanfeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049","observed_orcids":["https://orcid.org/0000-0002-6071-6049"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mordukhovich, Boris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Nguyen, Anh Vu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Anh Vu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078388333","display_name":"Lewei Zhao","orcid":"https://orcid.org/0000-0002-1050-3184","observed_orcids":["https://orcid.org/0000-0002-1050-3184"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Lewei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9833999872207642,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9833999872207642,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.0032999999821186066,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.002300000051036477,"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/l0-norm","display_name":"L0 norm","score":0.8130000233650208},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"multi-objective optimization","score":0.871999979019165},{"id":"https://openalex.org/keywords/proton-therapy","display_name":"proton therapy","score":0.7559999823570251},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"subgradient method","score":0.699999988079071},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"variational analysis","score":0.7860000133514404},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.8569999933242798},{"id":"https://openalex.org/keywords/cancer-radiotherapy","display_name":"cancer radiotherapy","score":0.6119999885559082}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7613999843597412},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6935999989509583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6722000241279602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5590000152587891},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.4523000121116638},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3887999951839447},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35109999775886536},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.31679999828338623},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.27160000801086426},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.26489999890327454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.06833","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.06833","pdf_url":"https://arxiv.org/pdf/2509.06833","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.2509.06833","doi":"https://doi.org/10.48550/arxiv.2509.06833","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.06833","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:2509.06833","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.06833","pdf_url":"https://arxiv.org/pdf/2509.06833","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415331523","https://openalex.org/W2038521488","https://openalex.org/W3017255278","https://openalex.org/W2987276217","https://openalex.org/W2261870747","https://openalex.org/W2034688818","https://openalex.org/W4286893626","https://openalex.org/W1547827494","https://openalex.org/W7098487294","https://openalex.org/W7160234366"],"abstract_inverted_index":{"The":[0,31,66],"paper":[1],"is":[2,16],"devoted":[3],"to":[4],"investigating":[5],"single-objective":[6],"and":[7,18,40,61,83],"multiobjective":[8,47],"optimization":[9],"problems":[10],"involving":[11],"the":[12,41,58,80,87],"$\\ell_0$-norm":[13],"function,":[14],"which":[15,74],"nonconvex":[17],"nondifferentiable.":[19],"Our":[20],"motivation":[21],"comes":[22],"from":[23],"proton":[24],"beam":[25],"therapy":[26],"models":[27],"in":[28,46],"cancer":[29],"research.":[30],"developed":[32],"approach":[33],"uses":[34],"subdifferential":[35],"tools":[36],"of":[37,57,79],"variational":[38],"analysis":[39],"Gerstewitz":[42],"(Tammer)":[43],"scalarization":[44],"function":[45],"optimization.":[48],"Based":[49],"on":[50],"this":[51],"machinery,":[52],"we":[53],"propose":[54],"several":[55],"algorithms":[56,82],"subgradient":[59],"type":[60],"conduct":[62],"their":[63,84],"convergence":[64],"analysis.":[65],"obtained":[67],"results":[68],"are":[69],"illustrated":[70],"by":[71],"numerical":[72],"examples,":[73],"reveal":[75],"some":[76],"characteristic":[77],"features":[78],"proposed":[81],"interactions":[85],"with":[86],"gradient":[88],"descent.":[89]},"counts_by_year":[],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}