{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:12:35Z","timestamp":1718089955379},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T00:00:00Z","timestamp":1346889600000},"content-version":"vor","delay-in-days":249,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"We investigate solving semidefinite programs (SDPs) with an interior point method called SDP\u2010CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP\u2010CUT iteratively refines\nthe feasible region to achieve the optimal solution. The algorithm uses Newton\u2019s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using\nNewton\u2032s method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP\u2010CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP\u2010CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most\nof the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP\u2010CUT are also discussed.<\/jats:p>","DOI":"10.1155\/2012\/946893","type":"journal-article","created":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T21:28:33Z","timestamp":1346966913000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers"],"prefix":"10.1155","volume":"2012","author":[{"given":"John","family":"Machacek","sequence":"first","affiliation":[]},{"given":"Shafiu","family":"Jibrin","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,9,6]]},"reference":[{"key":"e_1_2_9_1_2","volume-title":"Redundancy in Semidefinite Programming: Detection and Elimination of Redundant Linear Matrix Inequalities","author":"Jibrin S.","year":"2009"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/1038003"},{"key":"e_1_2_9_3_2","doi-asserted-by":"crossref","DOI":"10.1016\/S0168-9274(98)00098-1","article-title":"Applications of semidefinite programming","volume":"29","author":"Vandenberghe L.","year":"1999","journal-title":"Applied Numerical Mathematics"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0805002"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1090.0323"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1030.0046"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2006.08.002"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1958-10224-4"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/0108053"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386389"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580724"},{"key":"e_1_2_9_13_2","article-title":"The weighted analytic center for linear matrix inequalities","volume":"2","author":"Pressman I. S.","year":"2002","journal-title":"Journal of Inequalities in Pure and Applied Mathematics"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/040613378"},{"key":"e_1_2_9_15_2","article-title":"The boundary of weighted analytic centers for linear matrix inequalities","volume":"5","author":"Jibrin S.","year":"2004","journal-title":"Journal of Inequalities in Pure and Applied Mathematics"},{"key":"e_1_2_9_16_2","volume-title":"Numerical Optimization","author":"Nocedal J.","year":"2006"},{"key":"e_1_2_9_17_2","volume-title":"On the Implementation and Usage of SDPT3-a Matlab Software Package for Semidefinite-Quadratic-Linear Programming Version 4","author":"Tutuncu K. C.","year":"2006"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1080\/10556789908805769"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/946893.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/946893.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/946893","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:40:43Z","timestamp":1718088043000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/946893"}},"subtitle":[],"editor":[{"given":"James","family":"Buchanan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/946893"],"URL":"https:\/\/doi.org\/10.1155\/2012\/946893","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-10-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-24","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-09-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}