{"id":"https://openalex.org/W7225639705","doi":"https://doi.org/10.3390/mca31060252","title":"Functional-Analytic Inequalities and Matrix-Valued Energy Certificates for Convex Optimization","display_name":"Functional-Analytic Inequalities and Matrix-Valued Energy Certificates for Convex Optimization","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225639705","doi":"https://doi.org/10.3390/mca31060252"},"language":"en","primary_location":{"id":"doi:10.3390/mca31060252","doi":"https://doi.org/10.3390/mca31060252","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mca31060252","pdf_url":null,"source":{"id":"https://openalex.org/S4210201516","display_name":"Mathematical and Computational Applications","issn_l":"1300-686X","issn":["1300-686X","2297-8747"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 and Computational Applications","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/mca31060252","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115057871","display_name":"Ahad Hamoud Alotaibi","orcid":"https://orcid.org/0000-0003-3019-5139","observed_orcids":["https://orcid.org/0000-0003-3019-5139"]},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahad Hamoud Alotaibi","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3019-5139","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077288612","display_name":"Muhammad Waseem Asghar","orcid":"https://orcid.org/0000-0001-7538-2128","observed_orcids":["https://orcid.org/0000-0001-7538-2128"]},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["PK","ZA"],"is_corresponding":true,"raw_author_name":"Muhammad Waseem Asghar","raw_affiliation_strings":["Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg 2092, South Africa","International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7538-2128","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg 2092, South Africa","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077288612"],"corresponding_institution_ids":["https://openalex.org/I142204992","https://openalex.org/I24027795"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1689},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1689},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"6","first_page":"252","last_page":"252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-hadamard-fejer-inequality","display_name":"Hermite-Hadamard-Fej\u00e9r inequality","score":0.9200000166893005},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.49399998784065247},{"id":"https://openalex.org/keywords/simplices","display_name":"simplices","score":0.6869999766349792},{"id":"https://openalex.org/keywords/trace-bounds","display_name":"trace bounds","score":0.4779999852180481},{"id":"https://openalex.org/keywords/eigenvalue-bounds","display_name":"eigenvalue bounds","score":0.9869999885559082},{"id":"https://openalex.org/keywords/fejer-kernel","display_name":"Fej\u00e9r kernel","score":0.7760000228881836},{"id":"https://openalex.org/keywords/simultaneous-diagonalization","display_name":"simultaneous diagonalization","score":0.781000018119812},{"id":"https://openalex.org/keywords/non-commuting-operators","display_name":"non-commuting operators","score":0.7870000004768372},{"id":"https://openalex.org/keywords/functional-calculus","display_name":"functional calculus","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7554000020027161},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6653000116348267},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6000000238418579},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4794999957084656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46219998598098755},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.41260001063346863},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4101000130176544},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3840000033378601},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.35030001401901245},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3328000009059906},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3188000023365021},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3025999963283539},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.2818000018596649},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26589998602867126},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.2563000023365021}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/mca31060252","doi":"https://doi.org/10.3390/mca31060252","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mca31060252","pdf_url":null,"source":{"id":"https://openalex.org/S4210201516","display_name":"Mathematical and Computational Applications","issn_l":"1300-686X","issn":["1300-686X","2297-8747"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 and Computational Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/mca31060252","doi":"https://doi.org/10.3390/mca31060252","is_oa":true,"landing_page_url":"https://doi.org/10.3390/mca31060252","pdf_url":null,"source":{"id":"https://openalex.org/S4210201516","display_name":"Mathematical and Computational Applications","issn_l":"1300-686X","issn":["1300-686X","2297-8747"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"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 and Computational Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"},{"id":"https://openalex.org/F4320323959","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1523281138","https://openalex.org/W1601251575","https://openalex.org/W1999983074","https://openalex.org/W2042848202","https://openalex.org/W2130509920","https://openalex.org/W2296319761","https://openalex.org/W3023419123","https://openalex.org/W4214690803","https://openalex.org/W4234969842","https://openalex.org/W4249667877","https://openalex.org/W4255333822","https://openalex.org/W4292070096","https://openalex.org/W4391151970","https://openalex.org/W4409722992","https://openalex.org/W4410632472","https://openalex.org/W4410632477","https://openalex.org/W4414853691","https://openalex.org/W4416024739","https://openalex.org/W7125478460","https://openalex.org/W7215122066"],"related_works":["https://openalex.org/W1840414660","https://openalex.org/W2577981702","https://openalex.org/W4210900542","https://openalex.org/W4406419957","https://openalex.org/W2769003461","https://openalex.org/W2136311878","https://openalex.org/W1948402858","https://openalex.org/W2042793560","https://openalex.org/W2938856534","https://openalex.org/W2507554385"],"abstract_inverted_index":{"We":[0],"establish":[1],"explicitly":[2],"conditioned":[3],"multivariate":[4],"Hermite\u2013Hadamard\u2013Fej\u00e9r":[5],"(HH\u2013F)":[6],"upper":[7],"certificates":[8,117,126],"for":[9],"modified":[10],"(h,m)\u2013convexity":[11],"on":[12,118,127],"origin-anchored":[13],"boxes":[14,119],"and":[15,20,26,37,52,84,103,113,124,142,159,166,173,193],"simplices,":[16],"together":[17,120],"with":[18,121],"operator":[19,131],"matrix":[21],"counterparts":[22],"that":[23],"yield":[24],"trace-":[25],"eigenvalue-level":[27],"certificates.":[28],"To":[29],"keep":[30],"the":[31,35,46,49,63,68,130,133,146,171,176,190,200],"theory":[32],"mathematically":[33],"consistent,":[34],"scalar":[36],"box":[38],"analyses":[39],"are":[40,180],"organized":[41],"into":[42],"three":[43],"rigorous":[44,138],"regimes:":[45],"identity-generator":[47],"case,":[48,51],"affine-generator":[50],"a":[53,80,85],"genuinely":[54],"nonlinear":[55,157],"weighted":[56,86],"case":[57],"treated":[58],"through":[59],"w-adapted":[60],"convexity":[61],"along":[62],"pullback":[64,158],"path":[65],"induced":[66],"by":[67,99,139],"kernel":[69],"generator.":[70],"The":[71],"simplex":[72,160],"analysis":[73],"is":[74,136,149],"presented":[75],"in":[76],"two":[77],"layers,":[78],"namely":[79],"standard":[81],"radial":[82,87],"theorem":[83],"extension.":[88],"Within":[89],"this":[90],"structure,":[91],"we":[92],"introduce":[93],"tensorized":[94],"kernel-weighted":[95],"integral":[96],"operators":[97],"generated":[98],"coordinate-wise":[100],"maps":[101],"wi":[102],"Fej\u00e9r-symmetric":[104],"kernels,":[105],"recover":[106],"classical":[107],"rectangle":[108],"bounds":[109],"as":[110],"limiting":[111],"cases,":[112],"obtain":[114],"dimension-explicit":[115],"vertex":[116,125],"mixed":[122],"facet":[123],"simplices.":[128],"In":[129],"setting,":[132],"commuting":[134],"regime":[135,148],"fully":[137],"simultaneous":[140],"diagonalization":[141],"functional":[143],"calculus,":[144],"whereas":[145],"noncommuting":[147],"stated":[150],"only":[151],"under":[152],"explicit":[153,163],"operator-compatibility":[154],"hypotheses.":[155],"Verified":[156],"examples,":[161],"an":[162],"certificate-screening":[164],"step,":[165],"dimension-dependent":[167],"cost":[168],"calculations":[169],"demonstrate":[170],"reach":[172],"limitations":[174],"of":[175],"bounds.":[177],"Engineering":[178],"illustrations":[179],"analytic":[181],"proof-of-concept":[182],"calculations;":[183],"previously":[184],"reported":[185],"empirical":[186],"data-set":[187],"tables":[188],"lacking":[189],"requisite":[191],"scripts":[192],"split":[194],"indices":[195],"have":[196],"been":[197],"withdrawn":[198],"from":[199],"main":[201],"text.":[202]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}