{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T22:01:13Z","timestamp":1772661673812,"version":"3.50.1"},"reference-count":15,"publisher":"EDP Sciences","issue":"2","license":[{"start":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T00:00:00Z","timestamp":1649894400000},"content-version":"vor","delay-in-days":44,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,2,27]]},"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:p>In this paper we are generalizing the efficient kernel function with trigonometric barrier term given by (M. Bouafia, D. Benterki and A. Yassine, <jats:italic>J. Optim. Theory Appl.<\/jats:italic> <jats:bold>170<\/jats:bold> (2016) 528\u2013545). Using an elegant and simple analysis and under some easy to check conditions, we explore the best complexity result for the large update primal-dual interior point methods for linear optimization. This complexity estimate improves results obtained in (X. Li and M. Zhang, <jats:italic>Oper. Res. Lett.<\/jats:italic> <jats:bold>43<\/jats:bold> (2015) 471\u2013475; M.R. Peyghami and S.F. Hafshejani, <jats:italic>Numer. Algo.<\/jats:italic> <jats:bold>67<\/jats:bold> (2014) 33\u201348; M. Bouafia, D. Benterki and A. Yassine, <jats:italic>J. Optim. Theory Appl.<\/jats:italic> <jats:bold>170<\/jats:bold> (2016) 528\u2013545). Our comparative numerical experiments on some test problems consolidate and confirm our theoretical results according to which the new kernel function has promising applications compared to the kernel function given by (M. Bouafia and A. Yassine, <jats:italic>Optim. Eng.<\/jats:italic> <jats:bold>21<\/jats:bold> (2020) 651\u2013672). Moreover, the comparative numerical study that we have established favors our new kernel function better than other best trigonometric kernel functions (M. Bouafia, D. Benterki and A. Yassine, <jats:italic>J. Optim. Theory Appl.<\/jats:italic> <jats:bold>170<\/jats:bold> (2016) 528\u2013545; M. Bouafia and A. Yassine, <jats:italic>Optim. Eng.<\/jats:italic> <jats:bold>21<\/jats:bold> (2020) 651\u2013672).<\/jats:p>","DOI":"10.1051\/ro\/2022032","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T09:02:43Z","timestamp":1646125363000},"page":"731-750","source":"Crossref","is-referenced-by-count":9,"title":["Complexity analysis of primal-dual interior-point methods for linear optimization based on a new efficient Bi-parameterized kernel function with a trigonometric barrier term"],"prefix":"10.1051","volume":"56","author":[{"given":"Bouafia","family":"Mousaab","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yassine","family":"Adnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,4,14]]},"reference":[{"key":"R1","unstructured":"Bai Y.Q. and Roos C., A primal-dual interior point method based on a new kernel function with linear growth rate. In Proceedings of the 9th Australian Optimization Day, Perth, Australia (2002)."},{"key":"R2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1137\/S1052623403423114","volume":"15","author":"Bai","year":"2005","journal-title":"SIAM J. Optim."},{"key":"R3","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1007\/s11081-019-09467-w","volume":"21","author":"Bouafia","year":"2020","journal-title":"Optim. Eng."},{"key":"R4","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1007\/s10957-016-0895-0","volume":"170","author":"Bouafia","year":"2016","journal-title":"J. Optim. Theory Appl."},{"key":"R5","doi-asserted-by":"crossref","first-page":"3613","DOI":"10.1016\/j.cam.2011.05.036","volume":"236","author":"El Ghami","year":"2012","journal-title":"J. Comput. Appl. 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Math."},{"key":"R13","unstructured":"Roos C., Terlaky T. and Vial JPh, Theory and algorithms for linear optimization, In An interior point Approach, John Wiley & Sons, Chichester, UK (1997)."},{"key":"R14","unstructured":"Sonnevend G., An \u201canalytic center\u201d for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. In Vol. 84 of System Modelling and Optimization: Proceedings of the 12th IFIP-Conference, Budapest, Hungary, 1985, in: Lecture Notes in Control and Inform. Sci., edited by Prekopa A., Szelezsan J., Strazicky B.. Springer-Verlag, Berlin (1986) 866\u2013876."},{"key":"R15","doi-asserted-by":"crossref","unstructured":"Ye Y., Interior point algorithms. Theory and Analysis, John-Wiley Sons, Chichester, UK (1997).","DOI":"10.1002\/9781118032701"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2022032\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,14]],"date-time":"2022-04-14T08:03:10Z","timestamp":1649923390000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2022032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3]]},"references-count":15,"journal-issue":{"issue":"2"},"alternative-id":["ro210447"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2022032","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3]]}}}