{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:37:14Z","timestamp":1787341034753,"version":"3.56.0"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Recent interest in treespaces as well-founded mathematical domains for phylogenetic inference and statistical analysis for populations of anatomical trees has motivated research into efficient and rigorous methods for optimization problems on treespaces. A central problem in this area is computing an average of phylogenetic trees, which is equivalently characterized as the minimizer of the Fr\u00e9chet function. The Fr\u00e9chet mean can be used for statistical inference and exploratory data analysis; for example, it can be leveraged as a test statistic to compare groups via permutation tests, or to find trends in data over time via kernel smoothing. By analyzing the differential properties of the Fr\u00e9chet function along geodesics in treespace we obtained a theorem describing a decomposition of the derivative along a geodesic. This decomposition theorem is used to formulate optimality conditions which are used as a logical basis for an algorithm to verify relative optimality at points where the Fr\u00e9chet function gradient does not exist.<\/jats:p>","DOI":"10.1137\/15m1050914","type":"journal-article","created":{"date-parts":[[2018,4,3]],"date-time":"2018-04-03T11:33:09Z","timestamp":1522755189000},"page":"959-988","source":"Crossref","is-referenced-by-count":5,"title":["Relative Optimality Conditions and Algorithms for Treespace Fr\u00e9chet Means"],"prefix":"10.1137","volume":"28","author":[{"given":"Sean","family":"Skwerer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Scott","family":"Provan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. S.","family":"Marron","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-012-0091-3"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/140953393"},{"key":"atypb3","unstructured":"M. Bac\u030ca\u0301k,\n                      Convex Analysis and Optimization in Hadamard Spaces\n                      , De Gruyter Ser. Nonlinear Anal. Appl. 22, Walter de Gruyter, 2014."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0472-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2001.0759"},{"key":"atypb6","unstructured":"J. Felsenstein,\n                      Inferring Phylogenies\n                      , Sinauer Associates, 2004."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.265"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33454-2_19"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"O. Gascuel,\n                      Mathematics of Evolution and Phylogeny\n                      , Oxford University Press, 2005.","DOI":"10.1093\/oso\/9780198566106.001.0001"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1101\/gr.6339607"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/S0040-5809(02)00005-9"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"S. Holmes,\n                      Statistical approach to tests involving phylogenies\n                      , in Mathematics of Evolution and Phylogeny, O. Gascuel, ed., Oxford University Press, 2005, pp. 91-120.","DOI":"10.1093\/oso\/9780198566106.003.0004"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btq539"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdn087"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1093\/sysbio\/46.3.523"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2015.04.002"},{"key":"atypb17","unstructured":"M. Owen,\n                      personal communication\n                      , 2014."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2010.3"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/0314056"},{"key":"atypb20","unstructured":"S. Skwerer,\n                      Code for experiments and implementation of relative optimality conditions and algorithms for treespace Fre\u0301chet means\n                      ,https:\/\/github.com\/SeanSkwerer\/RelativeOptimalityConditionsTreespaceFrechetMeans, 2017."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-013-0473-0"},{"key":"atypb22","first-page":"357","author":"Sturm K.","year":"2003","journal-title":"AMS"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1050914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:02:38Z","timestamp":1787338958000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1050914"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/15M1050914"],"URL":"https:\/\/doi.org\/10.1137\/15m1050914","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}