{"id":"https://openalex.org/W2963336173","doi":"https://doi.org/10.1137/17m1140066","title":"Least Sparsity of $p$-Norm Based Optimization Problems with $p&gt;1$","display_name":"Least Sparsity of $p$-Norm Based Optimization Problems with $p&gt;1$","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963336173","doi":"https://doi.org/10.1137/17m1140066","mag":"2963336173"},"language":"en","primary_location":{"id":"doi:10.1137/17m1140066","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140066","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013733463","display_name":"Jinglai Shen","orcid":"https://orcid.org/0000-0003-2172-4182"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jinglai Shen","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003594160","display_name":"Seyedahmad Mousavi","orcid":null},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Seyedahmad Mousavi","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250","institution_ids":["https://openalex.org/I79272384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013733463"],"corresponding_institution_ids":["https://openalex.org/I79272384"],"apc_list":null,"apc_paid":null,"fwci":5.0669,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.96817622,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"28","issue":"3","first_page":"2721","last_page":"2751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":0.9933000206947327,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/mathematics","display_name":"Mathematics","score":0.6613348722457886},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6403734683990479},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6002863049507141},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5466665625572205},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.5445842742919922},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5081934928894043},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49134841561317444},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4286661446094513},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4119081199169159},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3765210509300232},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.36858856678009033},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.27238786220550537},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.17308908700942993}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6613348722457886},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6403734683990479},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6002863049507141},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5466665625572205},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.5445842742919922},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5081934928894043},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49134841561317444},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4286661446094513},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4119081199169159},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3765210509300232},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.36858856678009033},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.27238786220550537},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.17308908700942993},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1140066","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140066","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W638016179","https://openalex.org/W1973397215","https://openalex.org/W1974499748","https://openalex.org/W1984866494","https://openalex.org/W2003327187","https://openalex.org/W2012961725","https://openalex.org/W2024509716","https://openalex.org/W2030449718","https://openalex.org/W2033585806","https://openalex.org/W2035820295","https://openalex.org/W2072327470","https://openalex.org/W2078204800","https://openalex.org/W2083042020","https://openalex.org/W2083346837","https://openalex.org/W2084978503","https://openalex.org/W2093347109","https://openalex.org/W2119667497","https://openalex.org/W2122825543","https://openalex.org/W2126607811","https://openalex.org/W2135046866","https://openalex.org/W2145096794","https://openalex.org/W4234698323","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2138044000","https://openalex.org/W2330143608","https://openalex.org/W1988872022","https://openalex.org/W3196326125","https://openalex.org/W2157952460","https://openalex.org/W2117781171","https://openalex.org/W2160044169","https://openalex.org/W2946877649","https://openalex.org/W2041507040","https://openalex.org/W2748416747"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"$\\ell_p$-optimization":[2,121],"arising":[3],"from":[4],"sparse":[5,15,53,62],"optimization,":[6],"high-dimensional":[7],"data":[8],"analytics":[9],"and":[10,37,74,96,105,116,125,146],"statistics,":[11],"this":[12],"paper":[13,68],"studies":[14],"properties":[16,63],"of":[17,21,59,83,87,148],"a":[18,80,84,93],"wide":[19],"range":[20],"$p$-norm":[22,88,150],"based":[23,89,151],"optimization":[24,48,73,90,152],"problems":[25,49,91,153],"with":[26,122],"$p>1$,":[27,46],"including":[28],"generalized":[29],"basis":[30,32],"pursuit,":[31],"pursuit":[33],"denoising,":[34],"ridge":[35],"regression,":[36],"elastic":[38],"net.":[39],"It":[40],"is":[41,64],"well":[42,130],"known":[43],"that":[44,98],"when":[45],"these":[47],"lead":[50],"to":[51,71,78,120,133],"less":[52],"solutions.":[54],"However,":[55],"the":[56,60,108,134],"quantitative":[57],"characterization":[58],"adverse":[61],"not":[65],"available.":[66],"This":[67],"shows":[69],"how":[70],"exploit":[72],"matrix":[75],"analysis":[76,145],"techniques":[77],"develop":[79],"systematic":[81],"treatment":[82],"broad":[85],"class":[86],"for":[92,111,127],"general":[94,149],"$p>1$":[95],"show":[97],"their":[99],"optimal":[100],"solutions":[101],"attain":[102],"full":[103],"support,":[104],"thus":[106],"have":[107],"least":[109],"sparsity,":[110],"almost":[112],"all":[113],"measurement":[114,117],"matrices":[115],"vectors.":[118],"Comparison":[119],"$0<p\\le":[123],"1$":[124],"implications":[126],"robustness":[128],"as":[129,131],"extensions":[132],"complex":[135],"setting":[136],"are":[137],"also":[138],"given.":[139],"These":[140],"results":[141],"shed":[142],"light":[143],"on":[144],"computation":[147],"in":[154],"various":[155],"applications.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}