{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:43:01Z","timestamp":1777704181998,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T00:00:00Z","timestamp":1572393600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2020,3,4]]},"abstract":"<jats:p>In this paper, a modified nonmonotone QP-free method without penalty function or filter is proposed for inequality constrained optimization. There is only two or three systems of linear equations with the same coefficients are solved at each iteration. We obtain a fundamental direction and the corresponding multiplier by the first equation, and then make full use of Lagrangian function information and multiplier to bend the search direction appropriately and obtain the search direction by the second linear equation. Moreover, the acceptable criterion of trial points is relaxed by the modified nonmonotone linear search technique. Under mild conditions, the global convergence of the algorithm is proved. Numerical results are given at the end of the paper.<\/jats:p>","DOI":"10.3233\/jifs-190475","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T13:38:39Z","timestamp":1573220319000},"page":"3331-3342","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A modified nonmonotone QP-free method without penalty function or filter"],"prefix":"10.1177","volume":"38","author":[{"given":"Su","family":"Ke","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Hebei University, Key Laboratory of Machine Learning and Computational Intelligence, Baoding, P.R. China"}]},{"given":"Ren","family":"Lele","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Hebei University, Key Laboratory of Machine Learning and Computational Intelligence, Baoding, P.R. China"}]},{"given":"Ren","family":"Xiaohui","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Hebei University, Key Laboratory of Machine Learning and Computational Intelligence, Baoding, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2019,10,30]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"WilsonR.B. A simplicial algorithm for concave programming PhD thesis Graduate School of Business Administration Harvard University 1963."},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-014-0137-8"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(99)00176-9"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.08.009"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0326046"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499353935"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2016.1154947"},{"issue":"1","key":"e_1_3_2_9_2","first-page":"1","article-title":"Primal-dual interior point QP-free algorithm for nonlinear constrained optimization","volume":"239","author":"Jian J.B.","year":"2017","unstructured":"JianJ.B., ZengH.J., MaG.D. and ZhuZ.B., Primal-dual interior point QP-free algorithm for nonlinear constrained optimization, Journal of Inequalities and Applications 239(1) (2017), 1\u201325.","journal-title":"Journal of Inequalities and Applications"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022639306130"},{"issue":"1","key":"e_1_3_2_11_2","first-page":"17","article-title":"A simple primal-dual feasible interior-point method for nonlinear programming with monotone descent","volume":"25","author":"Sasan B.","year":"2003","unstructured":"SasanB. and Andr\u013a\u0119L.T., A simple primal-dual feasible interior-point method for nonlinear programming with monotone descent, Comput Optim Appl 25(1) (2003), 17\u201338.","journal-title":"Comput Optim Appl"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623401392123"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2006.04.019"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-010-7432-0"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2004.12.023"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100244"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403426544"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-011-9430-2"},{"issue":"3","key":"e_1_3_2_19_2","first-page":"31","article-title":"A new QP-free feasible method for inequality constrained Optimization","volume":"11","author":"Zhou Y.","year":"2007","unstructured":"ZhouY. and PuD.G., A new QP-free feasible method for inequality constrained Optimization, Operations Research Transactions 11(3) (2007), 31\u201343.","journal-title":"Operations Research Transactions"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2013.879587"},{"key":"e_1_3_2_21_2","unstructured":"DennisJ.E.Jr and SchnabelR.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations Prentice-Hall Englewoood Cliffs NJ 1983. Reprinted by SIAM Publications 1993."},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.08.013"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1137\/0723046"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-009-0287-4"},{"key":"e_1_3_2_25_2","doi-asserted-by":"crossref","unstructured":"HockW. and SchittkowskiK. Test examples for nonlinear programming codes Lecture Notes in Economics and Mathematical Systems Springer-Verlag Berlin Heidelberg New York 1981.","DOI":"10.1007\/978-3-642-48320-2"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190475","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-190475","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190475","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:40:39Z","timestamp":1777455639000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-190475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,30]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3,4]]}},"alternative-id":["10.3233\/JIFS-190475"],"URL":"https:\/\/doi.org\/10.3233\/jifs-190475","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,30]]}}}