{"id":"https://openalex.org/W2474764209","doi":"https://doi.org/10.1145/2897824.2925920","title":"Accelerated quadratic proxy for geometric optimization","display_name":"Accelerated quadratic proxy for geometric optimization","publication_year":2016,"publication_date":"2016-07-11","ids":{"openalex":"https://openalex.org/W2474764209","doi":"https://doi.org/10.1145/2897824.2925920","mag":"2474764209"},"language":"en","primary_location":{"id":"doi:10.1145/2897824.2925920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897824.2925920","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","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/A5074707764","display_name":"Shahar Z. Kovalsky","orcid":"https://orcid.org/0000-0001-8924-5538"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shahar Z. Kovalsky","raw_affiliation_strings":["Weizmann Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021644951","display_name":"Meirav Galun","orcid":null},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Meirav Galun","raw_affiliation_strings":["Weizmann Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039995559","display_name":"Yaron Lipman","orcid":null},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Yaron Lipman","raw_affiliation_strings":["Weizmann Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weizmann Institute of Science","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I53964585"],"apc_list":null,"apc_paid":null,"fwci":11.4643,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.99297403,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"35","issue":"4","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998000264167786,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9998000264167786,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7530609369277954},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5861434936523438},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4755920171737671},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.46824562549591064},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.466291606426239},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.46406540274620056},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4565853476524353},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.45363929867744446},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4424421787261963},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4342883825302124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4177485704421997},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38706955313682556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22094348073005676},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20223909616470337},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11720764636993408},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.10709956288337708}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7530609369277954},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5861434936523438},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4755920171737671},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.46824562549591064},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.466291606426239},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.46406540274620056},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4565853476524353},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.45363929867744446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4424421787261963},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4342883825302124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4177485704421997},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38706955313682556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22094348073005676},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20223909616470337},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11720764636993408},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.10709956288337708},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2897824.2925920","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2897824.2925920","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8899999856948853}],"awards":[{"id":"https://openalex.org/G4693840676","display_name":null,"funder_award_id":"307754","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G7480599527","display_name":null,"funder_award_id":"1284/12","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320335016","display_name":"Israeli Centers for Research Excellence","ror":"https://ror.org/03w2v9593"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W35783600","https://openalex.org/W581347801","https://openalex.org/W1600402929","https://openalex.org/W1600753972","https://openalex.org/W1621614599","https://openalex.org/W1946620893","https://openalex.org/W1976584051","https://openalex.org/W1982064072","https://openalex.org/W1987841290","https://openalex.org/W1988720110","https://openalex.org/W1998373192","https://openalex.org/W1999698136","https://openalex.org/W2000462146","https://openalex.org/W2018393413","https://openalex.org/W2032617361","https://openalex.org/W2051962838","https://openalex.org/W2053245826","https://openalex.org/W2064233581","https://openalex.org/W2076159000","https://openalex.org/W2082388593","https://openalex.org/W2094732964","https://openalex.org/W2095842012","https://openalex.org/W2100556411","https://openalex.org/W2101165370","https://openalex.org/W2101657948","https://openalex.org/W2109991971","https://openalex.org/W2113085766","https://openalex.org/W2121819464","https://openalex.org/W2123503703","https://openalex.org/W2124014126","https://openalex.org/W2133123311","https://openalex.org/W2141411966","https://openalex.org/W2151636374","https://openalex.org/W2160692760","https://openalex.org/W2166575557","https://openalex.org/W2169055648","https://openalex.org/W2184634347","https://openalex.org/W2235036220","https://openalex.org/W2250107905","https://openalex.org/W2293994889","https://openalex.org/W2295357537","https://openalex.org/W2461766609","https://openalex.org/W2595142274","https://openalex.org/W2596651194","https://openalex.org/W2913535645","https://openalex.org/W2936995161","https://openalex.org/W2963636509","https://openalex.org/W3000211808","https://openalex.org/W3029645440","https://openalex.org/W4206225701","https://openalex.org/W4210811533","https://openalex.org/W4241614188","https://openalex.org/W4244393449","https://openalex.org/W4285719527","https://openalex.org/W6601468598","https://openalex.org/W6734797129"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W2146343568","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2013643406","https://openalex.org/W2027972911","https://openalex.org/W2157978810","https://openalex.org/W4391547476","https://openalex.org/W2153649672"],"abstract_inverted_index":{"We":[0,51,167],"present":[1],"the":[2,13,46,85,119],"Accelerated":[3,158],"Quadratic":[4],"Proxy":[5],"(AQP)":[6],"-":[7],"a":[8,62,75,91,136,189],"simple":[9],"first-order":[10],"algorithm":[11],"for":[12,171,181],"optimization":[14,30,152],"of":[15,28,45,114,118,140],"geometric":[16,35],"energies":[17,36,47],"defined":[18],"over":[19,37,192],"triangular":[20],"and":[21,98,117,134,161,176,184],"tetrahedral":[22],"meshes.":[23],"The":[24],"main":[25],"stumbling":[26],"block":[27],"current":[29],"techniques":[31,153],"used":[32,154],"to":[33,43,61,72,83,89,131,142,149,187],"minimize":[34],"meshes":[38],"is":[39,56,81,112,128,145],"slow":[40],"convergence":[41],"due":[42,60],"ill-conditioning":[44,55],"at":[48],"their":[49],"minima.":[50],"observe":[52],"that":[53,111],"this":[54,144],"in":[57,66,87,106,146,174],"large":[58],"part":[59],"Laplacian-like":[63],"term":[64],"existing":[65],"these":[67],"energies.":[68],"Consequently,":[69],"we":[70],"suggest":[71],"locally":[73],"use":[74],"quadratic":[76],"polynomial":[77],"proxy,":[78],"whose":[79],"Hessian":[80],"taken":[82],"be":[84],"Laplacian,":[86],"order":[88],"achieve":[90],"preconditioning":[92],"effect.":[93],"This":[94],"already":[95],"improves":[96],"stability":[97],"convergence,":[99],"but":[100],"more":[101],"importantly":[102],"allows":[103],"incorporating":[104],"acceleration":[105],"an":[107],"almost":[108],"universal":[109],"way,":[110],"independent":[113],"mesh":[115,132,172],"size":[116],"specific":[120],"energy":[121],"considered.":[122],"Experiments":[123],"with":[124],"AQP":[125,170],"show":[126],"it":[127,186],"rather":[129],"insensitive":[130],"resolution":[133],"requires":[135],"nearly":[137],"constant":[138],"number":[139],"iterations":[141],"converge;":[143],"strong":[147],"contrast":[148],"other":[150],"popular":[151],"today":[155],"such":[156],"as":[157,178,180],"Gradient":[159],"Descent":[160],"Quasi-Newton":[162],"methods,":[163],"e.g.":[164],",":[165],"L-BFGS.":[166],"have":[168],"tested":[169],"deformation":[173],"2D":[175],"3D":[177],"well":[179],"surface":[182],"parameterization,":[183],"found":[185],"provide":[188],"considerable":[190],"speedup":[191],"common":[193],"baseline":[194],"techniques.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":14}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}
