{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:24:37Z","timestamp":1740122677129,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,7,7]],"date-time":"2018-07-07T00:00:00Z","timestamp":1530921600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006221","name":"United States - Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2012031"],"award-info":[{"award-number":["2012031"]}],"id":[{"id":"10.13039\/100006221","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2023464"],"award-info":[{"award-number":["2023464"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006221","name":"United States - Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2013003"],"award-info":[{"award-number":["2013003"]}],"id":[{"id":"10.13039\/100006221","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1162\/15","936\/16"],"award-info":[{"award-number":["1162\/15","936\/16"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2018,11]]},"DOI":"10.1007\/s10589-018-0021-3","type":"journal-article","created":{"date-parts":[[2018,7,7]],"date-time":"2018-07-07T05:48:34Z","timestamp":1530942514000},"page":"509-523","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Finding a best approximation pair of points for two polyhedra"],"prefix":"10.1007","volume":"71","author":[{"given":"Ron","family":"Aharoni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yair","family":"Censor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2946-7347","authenticated-orcid":false,"given":"Zilin","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,7]]},"reference":[{"key":"21_CR1","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/0022-247X(84)90163-X","volume":"103","author":"R Aharoni","year":"1984","unstructured":"Aharoni, R., Duchet, P., Wajnryb, B.: Successive projections on hyperplanes. J. Math. Anal. Appl. 103, 134\u2013138 (1984)","journal-title":"J. Math. Anal. Appl."},{"key":"21_CR2","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1006\/jmaa.1996.0308","volume":"202","author":"HH Bauschke","year":"1996","unstructured":"Bauschke, H.H.: The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space. J. Math. Anal. Appl. 202, 150\u2013159 (1996)","journal-title":"J. Math. Anal. Appl."},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BF01027691","volume":"1","author":"HH Bauschke","year":"1993","unstructured":"Bauschke, H.H., Borwein, J.M.: On the convergence of von Neumann\u2019s alternating projection algorithm for two sets. Set-Valued Anal. 1, 185\u2013212 (1993)","journal-title":"Set-Valued Anal."},{"key":"21_CR4","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1006\/jath.1994.1136","volume":"79","author":"HH Bauschke","year":"1994","unstructured":"Bauschke, H.H., Borwein, J.M.: Dykstra\u2019s alternating projection algorithm for two sets. J. Approx. Theory 79, 418\u2013443 (1994)","journal-title":"J. Approx. Theory"},{"key":"21_CR5","doi-asserted-by":"crossref","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. 2nd edn. Springer, Berlin (2017)","DOI":"10.1007\/978-3-319-48311-5"},{"key":"21_CR6","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.jat.2004.02.006","volume":"127","author":"HH Bauschke","year":"2004","unstructured":"Bauschke, H.H., Combettes, P.L., Luke, D.R.: Finding best approximation pairs relative to two closed convex sets in Hilbert spaces. J. Approx. Theory 127, 178\u2013192 (2004)","journal-title":"J. Approx. Theory"},{"key":"21_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/conm\/636\/12726","volume":"636","author":"HH Bauschke","year":"2015","unstructured":"Bauschke, H.H., Koch, V.R.: Projection methods: Swiss army knives for solving feasibility and best approximation problems with halfspaces. Contemp. Math. 636, 1\u201340 (2015)","journal-title":"Contemp. Math."},{"key":"21_CR8","volume-title":"Applied Iterative Methods","author":"CL Byrne","year":"2008","unstructured":"Byrne, C.L.: Applied Iterative Methods. A K Peters Ltd, Wellesley, MA (2008)"},{"key":"21_CR9","series-title":"Lecture Notes in Mathematics, vol. 2057","volume-title":"Iterative Methods for Fixed Point Problems in Hilbert Spaces","author":"A Cegielski","year":"2012","unstructured":"Cegielski, A.: Iterative Methods for Fixed Point Problems in Hilbert Spaces. Lecture Notes in Mathematics, vol. 2057. Springer, Berlin, Heidelberg (2012)"},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.laa.2005.10.006","volume":"416","author":"Y Censor","year":"2006","unstructured":"Censor, Y.: Computational acceleration of projection algorithms for the linear best approximation problem. Linear Algebra Appl. 416, 111\u2013123 (2006)","journal-title":"Linear Algebra Appl."},{"key":"21_CR11","doi-asserted-by":"publisher","first-page":"2343","DOI":"10.1080\/02331934.2014.957701","volume":"64","author":"Y Censor","year":"2015","unstructured":"Censor, Y., Cegielski, A.: Projection methods: an annotated bibliography of books and reviews. Optimization 64, 2343\u20132358 (2015)","journal-title":"Optimization"},{"key":"21_CR12","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.1007\/s10589-011-9401-7","volume":"51","author":"Y Censor","year":"2012","unstructured":"Censor, Y., Chen, W., Combettes, P.L., Davidi, R., Herman, G.T.: On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints. Comput. Optim. Appl. 51, 1065\u20131088 (2012)","journal-title":"Comput. Optim. Appl."},{"key":"21_CR13","unstructured":"Censor, Y., Zaknoon, M.: Algorithms and convergence results of projection methods for inconsistent feasibility problems: a review. Pure Appl. Funct. Anal. \n                    arXiv:1802.07529"},{"key":"21_CR14","volume-title":"Parallel Optimization: Theory, Algorithms, and Applications","author":"Y Censor","year":"1997","unstructured":"Censor, Y., Zenios, S.A.: Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, New York (1997)"},{"key":"21_CR15","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1090\/S0002-9939-1959-0105008-8","volume":"10","author":"W Cheney","year":"1959","unstructured":"Cheney, W., Goldstein, A.A.: Proximity maps for convex sets. Proc. Am. Math. Soc. 10, 448\u2013450 (1959)","journal-title":"Proc. Am. Math. Soc."},{"key":"21_CR16","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-1-4684-9298-9_2","volume-title":"Best Approximation in Inner Product Spaces","author":"Frank Deutsch","year":"2001","unstructured":"Deutsch, F.: Best Approximation in Inner Product Spaces. Springer, New York (2001)"},{"key":"21_CR17","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1080\/01621459.1983.10477029","volume":"78","author":"RL Dykstra","year":"1983","unstructured":"Dykstra, R.L.: An algorithm for restricted least squares regression. J. Am. Stat. Assoc. 78, 837\u2013842 (1983)","journal-title":"J. Am. Stat. Assoc."},{"key":"21_CR18","doi-asserted-by":"publisher","DOI":"10.1137\/9781611971941","volume-title":"Alternating Projection Methods","author":"R Escalante","year":"2011","unstructured":"Escalante, R., Raydan, M.: Alternating Projection Methods. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011)"},{"key":"21_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9180-5","volume-title":"Projectors and Projection Methods","author":"Aur\u00e9l Gal\u00e1ntai","year":"2004","unstructured":"Gal\u00e1ntai, A.: Projectors and Projection Methods. Kluwer Academic Publishers, Dordrecht (2004)"},{"key":"21_CR20","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","volume":"73","author":"B Halpern","year":"1967","unstructured":"Halpern, B.: Fixed points of nonexpanding maps. Bull. Am. Math. Soc. 73, 957\u2013961 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"21_CR21","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s11784-013-0097-4","volume":"12","author":"E Kopeck\u00e1","year":"2012","unstructured":"Kopeck\u00e1, E., Reich, S.: A note on alternating projections in Hilbert space. J. Fixed Point Theory Appl. 12, 41\u201347 (2012)","journal-title":"J. Fixed Point Theory Appl."},{"key":"21_CR22","first-page":"A1357","volume":"284","author":"PL Lions","year":"1977","unstructured":"Lions, P.L.: Approximation de points fixes de contractions. C. R. Acad. Sci. Paris S\u00e9r. A-B 284, A1357\u2013A1359 (1977)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A-B"},{"key":"21_CR23","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1137\/070681399","volume":"19","author":"DR Luke","year":"2008","unstructured":"Luke, D.R.: Finding best approximation pairs relative to a convex and prox-regular set in a Hilbert space. SIAM J. Optim. 19, 714\u2013739 (2008)","journal-title":"SIAM J. Optim."},{"key":"21_CR24","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/0012-365X(95)00055-2","volume":"154","author":"R Meshulam","year":"1996","unstructured":"Meshulam, R.: On products of projections. Discrete Math. 154, 307\u2013310 (1996)","journal-title":"Discrete Math."},{"key":"21_CR25","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1007\/BF01190119","volume":"58","author":"R Wittmann","year":"1992","unstructured":"Wittmann, R.: Approximation of fixed points of nonexpansive mappings. Arch. Math. (Basel) 58, 486\u2013491 (1992)","journal-title":"Arch. Math. (Basel)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-018-0021-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-018-0021-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-018-0021-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T15:01:06Z","timestamp":1569337266000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-018-0021-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,7]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["21"],"URL":"https:\/\/doi.org\/10.1007\/s10589-018-0021-3","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2018,7,7]]},"assertion":[{"value":"10 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2018","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}