{"id":"https://openalex.org/W97760719","doi":"https://doi.org/10.1007/978-1-4613-0469-2_3","title":"Support Function and Minkowski Addition of Non-Convex Sets","display_name":"Support Function and Minkowski Addition of Non-Convex Sets","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W97760719","doi":"https://doi.org/10.1007/978-1-4613-0469-2_3","mag":"97760719"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4613-0469-2_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-0469-2_3","pdf_url":null,"source":{"id":"https://openalex.org/S4210204999","display_name":"Computational imaging and vision","issn_l":"1381-6446","issn":["1381-6446","2542-8969"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320108","host_organization_name":"Springer Nature (Netherlands)","host_organization_lineage":["https://openalex.org/P4310320108","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature (Netherlands)","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Imaging and Vision","raw_type":"book-chapter"},"type":"book-chapter","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/A5079034254","display_name":"Michel Schmitt","orcid":"https://orcid.org/0000-0002-5003-1062"},"institutions":[{"id":"https://openalex.org/I4210148040","display_name":"Centre de G\u00e9osciences","ror":"https://ror.org/03kc13263","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210148040","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Michel Schmitt","raw_affiliation_strings":["Centre de G\u00e9ostatistique, 35, rue Saint Honor\u00e9, 77305, Fontainebleau-Cedex, France"],"affiliations":[{"raw_affiliation_string":"Centre de G\u00e9ostatistique, 35, rue Saint Honor\u00e9, 77305, Fontainebleau-Cedex, France","institution_ids":["https://openalex.org/I4210148040"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079034254"],"corresponding_institution_ids":["https://openalex.org/I4210148040"],"apc_list":null,"apc_paid":null,"fwci":1.2507,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75290391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"15","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9771000146865845,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9771000146865845,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.968999981880188,"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":0.960099995136261,"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/transpose","display_name":"Transpose","score":0.7647053003311157},{"id":"https://openalex.org/keywords/support-function","display_name":"Support function","score":0.7534078359603882},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.655940592288971},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.5956825017929077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5693148970603943},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5625494718551636},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5123320817947388},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5089929103851318},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5048297047615051},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49994444847106934},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.44225984811782837},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30712175369262695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19530147314071655},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.14523038268089294},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1209021806716919},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04903450608253479}],"concepts":[{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.7647053003311157},{"id":"https://openalex.org/C173278390","wikidata":"https://www.wikidata.org/wiki/Q3075191","display_name":"Support function","level":5,"score":0.7534078359603882},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.655940592288971},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.5956825017929077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5693148970603943},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5625494718551636},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5123320817947388},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5089929103851318},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5048297047615051},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49994444847106934},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.44225984811782837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30712175369262695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19530147314071655},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.14523038268089294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1209021806716919},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04903450608253479},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4613-0469-2_3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-0469-2_3","pdf_url":null,"source":{"id":"https://openalex.org/S4210204999","display_name":"Computational imaging and vision","issn_l":"1381-6446","issn":["1381-6446","2542-8969"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320108","host_organization_name":"Springer Nature (Netherlands)","host_organization_lineage":["https://openalex.org/P4310320108","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature (Netherlands)","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Imaging and Vision","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W132420851","https://openalex.org/W1525537197","https://openalex.org/W1593939129","https://openalex.org/W1996931690","https://openalex.org/W2164741953","https://openalex.org/W2480555354","https://openalex.org/W2795869619","https://openalex.org/W2911302472","https://openalex.org/W3041834803","https://openalex.org/W4230982142","https://openalex.org/W6633687401","https://openalex.org/W6649648916","https://openalex.org/W6750349569"],"related_works":["https://openalex.org/W2286777929","https://openalex.org/W4293050169","https://openalex.org/W2950428426","https://openalex.org/W2053229390","https://openalex.org/W960999769","https://openalex.org/W4211088175","https://openalex.org/W4309277470","https://openalex.org/W2936973291","https://openalex.org/W4288372977","https://openalex.org/W2090226889"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}