{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,1]],"date-time":"2023-07-01T04:17:18Z","timestamp":1688185038403},"reference-count":24,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T00:00:00Z","timestamp":1688083200000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,6,12]]},"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for <jats:italic>P<\/jats:italic><jats:sub>*<\/jats:sub>(<jats:italic>\u03ba<\/jats:italic>)-horizontal linear complementarity problem based on this kernel function, with parameters <jats:italic>p<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> &gt; 0 for all <jats:italic>i<\/jats:italic>\u00a0\u2208\u00a01,\u00a02,\u00a0,\u00a0<jats:italic>m<\/jats:italic>, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (<jats:bold>IPM<\/jats:bold>) for <jats:italic>P<\/jats:italic><jats:sub>*<\/jats:sub>(<jats:italic>\u03ba<\/jats:italic>)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, <jats:bold>O<\/jats:bold>((1 + 2\u03ba)\u221a<jats:italic>n<\/jats:italic>(log <jats:italic>n<\/jats:italic>)log <jats:italic>n<\/jats:italic>\/\u03f5) and <jats:bold>O<\/jats:bold>((1 + 2\u03ba)\u221a<jats:italic>n<\/jats:italic> log <jats:italic>n<\/jats:italic>\/\u03f5) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.<\/jats:p>","DOI":"10.1051\/ro\/2023094","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T18:56:20Z","timestamp":1686768980000},"page":"1599-1616","source":"Crossref","is-referenced-by-count":0,"title":["An efficient multi parametric kernel function for large and small-update methods interior point algorithm for <i>P<\/i><sub>*<\/sub>(<i>\u03ba<\/i>)-horizontal linear complementarity problem"],"prefix":"10.1051","volume":"57","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":[[2023,6,30]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s40305-015-0070-6","volume":"3","author":"Asadi","year":"2015","journal-title":"J. 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