{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T17:31:49Z","timestamp":1779903109277,"version":"3.53.1"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified BFGS methods with function value information is presented. The new methods satisfy some new weak secant equations and there is a parameter \u03b3 in the update formulae which ranges from zero to one. The global and local superlinear convergence properties of the new modified BFGS methods are proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the methods in the proposed class perform well. Ensuring the sufficient positive definiteness of the updating matrices, an adaptive BFGS quasi-Newton method by dynamically choosing the parameter \u03b3 is proposed, which may be competitive with other BFGS modifications.<\/jats:p>","DOI":"10.1142\/s0217595913500243","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T09:36:10Z","timestamp":1380620170000},"page":"1350024","source":"Crossref","is-referenced-by-count":2,"title":["A CLASS OF MODIFIED BFGS METHODS WITH FUNCTION VALUE INFORMATION FOR UNCONSTRAINED OPTIMIZATION"],"prefix":"10.1142","volume":"30","author":[{"given":"HAO","family":"LIU","sequence":"first","affiliation":[{"name":"College of Sciences, Nanjing University of Technology, Nanjing, Jiangsu, 210009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"HAI-JUN","family":"WANG","sequence":"additional","affiliation":[{"name":"College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"XIAO-YAN","family":"QIAN","sequence":"additional","affiliation":[{"name":"College of Sciences, Nanjing University of Technology, Nanjing, Jiangsu, 210009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"QING-SHENG","family":"SHI","sequence":"additional","affiliation":[{"name":"College of Sciences, Nanjing University of Technology, Nanjing, Jiangsu, 210009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2013,12,19]]},"reference":[{"key":"rf1","first-page":"63","volume":"11","author":"Al-Baali M.","journal-title":"AMO\u2013Advanced Modeling and Optimization"},{"key":"rf2","author":"Al-Baali M.","journal-title":"Computational Optimization and Applications"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/0914080"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/8.1.141"},{"key":"rf5","first-page":"123","volume":"20","author":"Bongartz I.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1967-0224273-2"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/0724077"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1137\/0726042"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401383455"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1014838419611"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/0717023"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/0719025"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592055"},{"key":"rf14","first-page":"546","volume":"19","author":"Dennis J. E.","journal-title":"SIAM Review"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1137\/1021091"},{"key":"rf16","first-page":"357","volume":"50","author":"Ford J. A.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00178-6"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00540-9"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1080\/10556780701646360"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623402418991"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494266365"},{"key":"rf22","doi-asserted-by":"crossref","unstructured":"R. S.\u00a0Schnabel, Nonlinear Programming, The State of the Art, eds. A.\u00a0Bachem, M.\u00a0Grotschel and B.\u00a0Krote (Springer-Verlag, Berlin, 1983)\u00a0pp. 417\u2013438.","DOI":"10.1007\/978-3-642-68874-4_17"},{"key":"rf23","first-page":"62","volume":"208","author":"Wang H. J.","journal-title":"Applied Mathematics and Comptation"},{"key":"rf24","first-page":"1","volume":"11","author":"Wang H. J.","journal-title":"OR Transactions"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.08.027"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012959223138"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/11.3.325"},{"key":"rf28","first-page":"95","volume":"13","author":"Yuan Y. X.","journal-title":"Journal of Computational Mathematics"},{"key":"rf29","volume-title":"Optimization Theory and Methods","author":"Yuan Y. X.","year":"1997"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021898630001"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00713-5"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595913500243","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T13:57:01Z","timestamp":1646661421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595913500243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":31,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2013,12,19]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S0217595913500243"],"URL":"https:\/\/doi.org\/10.1142\/s0217595913500243","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}