{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T16:44:42Z","timestamp":1715618682419},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q \u2208 V we consider the general linear complementarity problem LCP (L, K, q) on a proper cone K \u2286 V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP (L, K, q), whenever L is strongly monotone. Lipschitz constants of L is vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.<\/jats:p>","DOI":"10.1142\/s0219198913400355","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T08:08:03Z","timestamp":1372752483000},"page":"1340035","source":"Crossref","is-referenced-by-count":2,"title":["SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS"],"prefix":"10.1142","volume":"15","author":[{"given":"A.","family":"CHANDRASHEKARAN","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Central University of Tamil Nadu, Thiruvarur-610 004, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"PARTHASARATHY","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, Chennai Centre, Chennai - 600 029, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"VETRIVEL","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,11,18]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2006.01.003"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/0471787779"},{"key":"rf4","volume-title":"The Linear Complimentarity Problem","author":"Cottle R. W.","year":"1992"},{"key":"rf5","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"Facchinei F.","year":"2003"},{"key":"rf6","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"Facchinei F.","year":"2003"},{"key":"rf7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on Symmetric Cones","author":"Faraut J.","year":"1994"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011387"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(03)00425-7"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/06065943X"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.03.028"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934094"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494269035"},{"key":"rf14","first-page":"326","volume":"2","author":"Parthasarathy T.","journal-title":"Math. Oper. Res."}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219198913400355","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T16:15:00Z","timestamp":1715616900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219198913400355"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,18]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,11,18]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S0219198913400355"],"URL":"https:\/\/doi.org\/10.1142\/s0219198913400355","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"value":"0219-1989","type":"print"},{"value":"1793-6675","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,18]]}}}