{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:46:01Z","timestamp":1773251161627,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2018,6]]},"abstract":"<jats:p> A sequentially semidefinite programming method is proposed for solving nonlinear semidefinite programming problem (NLSDP). Inspired by the sequentially quadratic programming (SQP) method, the algorithm generates a search direction by solving a quadratic semidefinite programming subproblem at each iteration. The [Formula: see text] exact penalty function and a line search strategy are used to determine whether the trial step can be accepted or not. Under mild assumptions, the proposed algorithm is globally convergent. In order to avoid the Maratos effect, we present a modified SQP-type algorithm with the second-order correction step and prove that the fast local superlinear convergence can be obtained under the strict complementarity and the second-order sufficient condition with the sigma term. Finally, some numerical experiments are given to show the effectiveness of the algorithm. <\/jats:p>","DOI":"10.1142\/s0217595918500094","type":"journal-article","created":{"date-parts":[[2018,1,18]],"date-time":"2018-01-18T07:11:22Z","timestamp":1516259482000},"page":"1850009","source":"Crossref","is-referenced-by-count":8,"title":["An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming"],"prefix":"10.1142","volume":"35","author":[{"given":"Qi","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China"}]},{"given":"Zhongwen","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Soochow University, Suzhou 215006, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2018,5,31]]},"reference":[{"key":"S0217595918500094BIB001","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.807"},{"key":"S0217595918500094BIB002","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010091831812"},{"key":"S0217595918500094BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718829"},{"key":"S0217595918500094BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"S0217595918500094BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01593788"},{"key":"S0217595918500094BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S0217595915400060"},{"key":"S0217595918500094BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402417298"},{"key":"S0217595918500094BIB008","doi-asserted-by":"publisher","DOI":"10.1080\/00207170010010605"},{"key":"S0217595918500094BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-006-0028-x"},{"key":"S0217595918500094BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900373483"},{"key":"S0217595918500094BIB011","first-page":"205","volume":"31","author":"Garc\u00e9s R","year":"2012","journal-title":"Computional and Applied Mathematics"},{"issue":"2","key":"S0217595918500094BIB012","first-page":"297","volume":"29","author":"G\u00f3mez W","year":"2010","journal-title":"Computational and Applied Mathematics"},{"key":"S0217595918500094BIB013","doi-asserted-by":"publisher","DOI":"10.1080\/1055678031000098773"},{"key":"S0217595918500094BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-006-9102-z"},{"key":"S0217595918500094BIB016","doi-asserted-by":"publisher","DOI":"10.1515\/JAA.2009.149"},{"key":"S0217595918500094BIB017","doi-asserted-by":"publisher","DOI":"10.1080\/10556780008805787"},{"key":"S0217595918500094BIB018","series-title":"Springer Series in Operations Research","volume-title":"Numerical Optimization","author":"Nocedal J","year":"2006"},{"key":"S0217595918500094BIB019","doi-asserted-by":"publisher","DOI":"10.1137\/0325051"},{"key":"S0217595918500094BIB020","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1060.0195"},{"key":"S0217595918500094BIB022","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896303430"},{"key":"S0217595918500094BIB023","first-page":"1","volume":"1","author":"Wang Y","year":"2008","journal-title":"Journal of Inequalities and Applications"},{"key":"S0217595918500094BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0449-z"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595918500094","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:56:34Z","timestamp":1565132194000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595918500094"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,31]]},"references-count":22,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2018,5,31]]},"published-print":{"date-parts":[[2018,6]]}},"alternative-id":["10.1142\/S0217595918500094"],"URL":"https:\/\/doi.org\/10.1142\/s0217595918500094","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,31]]}}}