{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,7]],"date-time":"2023-10-07T11:42:27Z","timestamp":1696678947705},"reference-count":32,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T00:00:00Z","timestamp":1696550400000},"content-version":"vor","delay-in-days":35,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,8,12]]},"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p>We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function <jats:italic>\u03c8<\/jats:italic>(<jats:italic>t<\/jats:italic>) = <jats:italic>t<\/jats:italic>7\\4. Furthermore, we show that the algorithm finds the <jats:italic>\u03f5<\/jats:italic>-optimal solution of the underlying problem in polynomial time, namely <jats:italic>O<\/jats:italic>(\u221a<jats:italic>n<\/jats:italic>log(<jats:italic>n<\/jats:italic>+3\\7\u221a2)) iterations. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.<\/jats:p>","DOI":"10.1051\/ro\/2023127","type":"journal-article","created":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T18:58:44Z","timestamp":1693853924000},"page":"2473-2491","source":"Crossref","is-referenced-by-count":0,"title":["Interior-point algorithm for linear programming based on a new descent direction"],"prefix":"10.1051","volume":"57","author":[{"given":"Zaoui","family":"Billel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benterki","family":"Djamel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kraria","family":"Aicha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raouache","family":"Hadjer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2023,10,6]]},"reference":[{"key":"R1","first-page":"61","volume":"49","author":"Achache","year":"2004","journal-title":"Stud. Univ. Babe.s-Bolyai Math. Ser. Inform."},{"key":"R2","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1590\/S0101-82052006000100005","volume":"25","author":"Achache","year":"2006","journal-title":"Comput. Appl. Math."},{"key":"R3","first-page":"48","volume":"LVII","author":"Achache","year":"2012","journal-title":"Stud. Univ. Babe.s-Bolyai Math. Ser. Inform."},{"key":"R4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1137\/S1052623403423114","volume":"15","author":"Bai","year":"2005","journal-title":"SIAM. J. Optim."},{"key":"R5","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1051\/ro\/2015056","volume":"50","author":"Bouafia","year":"2016","journal-title":"RAIRO: OR"},{"key":"R6","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":"R7","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1080\/02331934.2020.1751156","volume":"70","author":"Boudjellal","year":"2021","journal-title":"Optimization"},{"key":"R8","first-page":"51","volume":"5","author":"Darvay","year":"2003","journal-title":"Adv. Model. Optim."},{"key":"R9","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1007\/s11590-017-1171-4","volume":"12","author":"Darvay","year":"2018","journal-title":"Optim. Lett."},{"key":"R10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10998-016-0119-2","volume":"73","author":"Darvay","year":"2016","journal-title":"Period. Math. Hungar."},{"key":"R11","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ejor.2021.08.039","volume":"298","author":"Darvay","year":"2022","journal-title":"Eur. J. Oper. Res."},{"key":"R12","unstructured":"Deng Q., Feng Q., Gao W., Ge D., Jiang B., Jiang Y., Liu J., Liu T., Xue C., Ye Y. and Zhang C., New developments of ADMM-based interior point methods for linear programming and conic programming. Preprint arXiv:2209.01793 (2023)."},{"key":"R13","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. Math."},{"key":"R14","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1080\/02331930903104382","volume":"59","author":"Feng","year":"2010","journal-title":"Optimization"},{"key":"R15","first-page":"10","volume":"3","author":"Gay","year":"1985","journal-title":"Math. Program. Soc. COAL Newslett."},{"key":"R16","doi-asserted-by":"crossref","first-page":"3955","DOI":"10.1051\/ro\/2022192","volume":"56","author":"Guerra","year":"2022","journal-title":"RAIRO:OR"},{"key":"R17","unstructured":"L.L.C. Gurobi Optimization, Gurobi optimizer reference manual (Gurobi Optimization, LLC) (2022)."},{"key":"R18","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1080\/01630563.2019.1598430","volume":"40","author":"Kheirfam","year":"2019","journal-title":"Numer. Funct. Anal. Optim."},{"key":"R19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.17535\/crorr.2019.0023","volume":"10","author":"Kheirfam","year":"2019","journal-title":"Croat. Oper. Res. Rev."},{"key":"R20","unstructured":"Kheirfam B., A new search direction for full-Newton step infeasible interior-point method in linear optimization. Preprint arXiv:2102.07223v1 (2021)."},{"key":"R21","doi-asserted-by":"crossref","first-page":"233","DOI":"10.2298\/YJOR120904006K","volume":"25","author":"Kheirfam","year":"2015","journal-title":"Yugosl. J. Oper. Res."},{"key":"R22","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.orl.2015.06.013","volume":"43","author":"Li","year":"2015","journal-title":"Oper. Res. Lett."},{"key":"R23","doi-asserted-by":"crossref","unstructured":"Lin T., Ma S., Ye Y. and Zhang S., An ADMM-based interior-point method for large-scale linear programming. Optim. Methods Softw. 36 (2021).","DOI":"10.1080\/10556788.2020.1821200"},{"key":"R24","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.cam.2013.04.039","volume":"255","author":"Peyghami","year":"2014","journal-title":"J. Comput. Appl. Math."},{"key":"R25","unstructured":"Roos C., Terlaky T. and Vial J.P., Theory and algorithms for linear optimization, an interior approach. John Wiley and Sons, Chichester, UK (1997)."},{"key":"R26","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1080\/02331934.2018.1432610","volume":"67","author":"Tak\u00e0cs","year":"2018","journal-title":"Optimization"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"Sonnevend G., An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming, edited by A. Prekopa, J. Szelezsan and B. Strazicky. In: Lect. Notes Control Inf. Sci. 84 (1986) 866\u2013876.","DOI":"10.1007\/BFb0043914"},{"key":"R28","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.jmaa.2008.12.016","volume":"353","author":"Wang","year":"2009","journal-title":"J. Math. Anal. Appl."},{"key":"R29","first-page":"1047","volume":"215","author":"Wang","year":"2009","journal-title":"Appl. Math. Comput."},{"key":"R30","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1007\/s10957-012-0013-x","volume":"154","author":"Wang","year":"2012","journal-title":"J. Optim. Theory Appl."},{"key":"R31","doi-asserted-by":"crossref","unstructured":"Wright S.J., Primal-dual interior point methods, Copyright by SIAM. (1997).","DOI":"10.1137\/1.9781611971453"},{"key":"R32","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.orl.2011.06.006","volume":"39","author":"Zhang","year":"2011","journal-title":"Oper. Res. Lett."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T08:00:37Z","timestamp":1696579237000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":32,"journal-issue":{"issue":"5"},"alternative-id":["ro220554"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2023127","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9]]}}}