{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:41:23Z","timestamp":1787341283864,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100012550","name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","doi-asserted-by":"publisher","award":["2024-1.2.3-HU-RIZONT-2024-00030"],"award-info":[{"award-number":["2024-1.2.3-HU-RIZONT-2024-00030"]}],"id":[{"id":"10.13039\/501100012550","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Austrian-Hungarian Action Foundation","award":["116__amp__#x00F6"],"award-info":[{"award-number":["116__amp__#x00F6"]}]},{"name":"Austrian-Hungarian Action Foundation","award":["u8"],"award-info":[{"award-number":["u8"]}]},{"DOI":"10.13039\/501100003825","name":"Hungarian Academy of Sciences","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003825","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ministry of Culture and Innovation of Hungary","award":["142154"],"award-info":[{"award-number":["142154"]}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-23-1-0370"],"award-info":[{"award-number":["FA9550-23-1-0370"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006347","name":"Universitatea Babe\u0219-Bolyai","doi-asserted-by":"publisher","award":["AGC33859\/30.08.2024"],"award-info":[{"award-number":["AGC33859\/30.08.2024"]}],"id":[{"id":"10.13039\/501100006347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003825","name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003825","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present an interior-point algorithm for [Formula: see text]-linear complementarity problems, based on a barrier function defined by a new class of univariate kernel functions, called standard kernel functions (SKFs). A comprehensive and unified complexity analysis of the algorithm is provided,\u00a0and a general procedure is developed to determine the iteration bounds for long-step and short-step versions of the method for the entire class of SKFs. We illustrate the general procedure by determining the iteration bounds for several parametric SKFs, which include, as special cases, all eligible kernel functions from the literature that have rational or exponential barrier terms. In all cases, we match the best iteration bounds obtained in the literature for these special cases of SKFs.<\/jats:p>","DOI":"10.1137\/24m1691892","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T07:34:10Z","timestamp":1779867250000},"page":"887-911","source":"Crossref","is-referenced-by-count":0,"title":["Comprehensive Analysis of Kernel-Based Interior-Point Methods for the \\({P}_{{*}}{(\\kappa )}\\)-LCP"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1094-9837","authenticated-orcid":true,"given":"Zsolt","family":"Darvay","sequence":"first","affiliation":[{"name":"Babe\u015f-Bolyai University, Cluj-Napoca, Romania."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3688-412X","authenticated-orcid":true,"given":"Marianna","family":"E.-Nagy","sequence":"additional","affiliation":[{"name":"Corvinus Centre for Operations Research, Corvinus University of Budapest, H-1093 Budapest, Hungary."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3840-4599","authenticated-orcid":true,"given":"Goran","family":"Lesaja","sequence":"additional","affiliation":[{"name":"Corvinus Centre for Operations Research, Corvinus University of Budapest, H-1093 Budapest, Hungary."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3867-0304","authenticated-orcid":true,"given":"Petra Ren\u00e1ta","family":"Rig\u00f3","sequence":"additional","affiliation":[{"name":"Corvinus Centre for Operations Research, Corvinus University of Budapest, H-1093 Budapest, Hungary."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7138-2921","authenticated-orcid":true,"given":"Anita","family":"Varga","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/040604492"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s101070050027"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1080\/10556789708805657"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401398132"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403423114"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-008-9389-z"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.04.060"},{"key":"ref8","unstructured":"S. J. Chung, A Note on the Complexity of the LCP: The LCP Is Strongly NP-complete, Technical Report 792, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI, 1979."},{"key":"ref9","volume-title":"The Linear Complementarity Problem","author":"Cottle R. W.","year":"1992"},{"key":"ref10","first-page":"51","volume":"5","author":"Darvay Zs.","year":"2003","journal-title":"Adv. Model. Optim."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/19M1248972"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10998-016-0119-2"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2018.1492938"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-018-0524-0"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-017-1171-4"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.17516\/1997-1397-2019-12-2-160-172"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-023-02280-7"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-022-02121-z"},{"key":"ref19","unstructured":"M. E.Nagy and L. V\u00e9gh, Handicap Reduction for Linear Complementarity Problems, manuscript, 2025\n                      ."},{"key":"ref20","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"Facchinei F.","year":"2003"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-023-02232-1"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-54509-3"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/090766735"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/050623723"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/0806001"},{"key":"ref26","first-page":"245","volume-title":"High Performance Optimization","author":"Peng J.","year":"1999"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019280614748"},{"key":"ref28","volume-title":"Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms","author":"Peng J.","year":"2002"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0472-9"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1080\/10556780512331318038"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718812"},{"key":"ref32","volume-title":"Interior Point Methods for Linear Optimization","author":"Roos C.","year":"2005"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(96)90005-1"},{"key":"ref34","first-page":"19","volume":"1","author":"Wang G.","year":"2017","journal-title":"Appl. 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