{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T23:10:56Z","timestamp":1774998656010,"version":"3.50.1"},"publisher-location":"Cham","reference-count":7,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032157904","type":"print"},{"value":"9783032157911","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-15791-1_5","type":"book-chapter","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:38:53Z","timestamp":1774996733000},"page":"65-75","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convexity Measurement of\u00a0the\u00a0Barrier Parameter Functional of\u00a0Self-concordant Barriers"],"prefix":"10.1007","author":[{"given":"Vitali","family":"Pirau","sequence":"first","affiliation":[]},{"given":"Roland","family":"Hildebrand","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"G\u00fcler, O.: Characterization of the barrier parameter of homogeneous convex cones. Math. Program. 81, 55\u201376 (1998)","DOI":"10.1007\/BF01584844"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Hildebrand, R.: A lower bound on the barrier parameter of barriers for convex cones. Math. Prog. 142, 311\u2013329 (2013)","DOI":"10.1007\/s10107-012-0576-1"},{"key":"5_CR3","doi-asserted-by":"crossref","unstructured":"Nesterov, Y.E., Todd, M.J.: Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22(1), 1\u201342 (1997)","DOI":"10.1287\/moor.22.1.1"},{"key":"5_CR4","doi-asserted-by":"crossref","unstructured":"Nesterov, Y.: Towards non-symmetric conic optimization. Optim. Methods Softw. 27(4-5), 893\u2013917 (2012)","DOI":"10.1080\/10556788.2011.567270"},{"key":"5_CR5","doi-asserted-by":"crossref","unstructured":"Nesterov, Y., Nemirovskii, A.: Interior-point Polynomial Algorithms in Convex Programming, SIAM Stud. Appl. Math., vol.\u00a013. SIAM, Philadelphia (1994)","DOI":"10.1137\/1.9781611970791"},{"key":"5_CR6","doi-asserted-by":"crossref","unstructured":"Pirau, V., Hildebrand, R.: Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers. In: Kochetov, Y., Khachay, M., Eremeev, A., Pardalos, P. (eds), Lecture Notes in Computer Science, vol 15681, Springer, pp. 80\u201392, (2025)","DOI":"10.1007\/978-3-031-97077-1_6"},{"key":"5_CR7","doi-asserted-by":"crossref","unstructured":"Uhlmann, A.: Roofs and convexity. Entropy 12, 1799\u20131832 (2010)","DOI":"10.3390\/e12071799"}],"container-title":["Lecture Notes in Computer Science","Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-15791-1_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:38:54Z","timestamp":1774996734000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-15791-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032157904","9783032157911"],"references-count":7,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-15791-1_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"1 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"OPTIMA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Optimization and Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Petrovac","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montenegro","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"optima2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conf-optima.ru","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}