{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T23:21:24Z","timestamp":1769210484007,"version":"3.49.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T00:00:00Z","timestamp":1555977600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100010909","name":"Young Scientists Fund","doi-asserted-by":"publisher","award":["11401450"],"award-info":[{"award-number":["11401450"]}],"id":[{"id":"10.13039\/501100010909","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11861026"],"award-info":[{"award-number":["11861026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871383"],"award-info":[{"award-number":["11871383"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671338"],"award-info":[{"award-number":["61671338"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s40314-019-0856-y","type":"journal-article","created":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T09:04:24Z","timestamp":1556010264000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A nonmonotone smoothing Newton method for system of nonlinear inequalities based on a new smoothing function"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9912-2248","authenticated-orcid":false,"given":"Yuan","family":"Liuyang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cui","family":"Fei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wan","family":"Zhongping","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Weigang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wang","family":"Wenbo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,4,23]]},"reference":[{"issue":"5","key":"856_CR1","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/BF01436488","volume":"21","author":"JW Daniel","year":"1973","unstructured":"Daniel JW (1973) Newton\u2019s Method for Nonlinear Inequalities. Numerische Mathematik 21(5):381\u2013387","journal-title":"Numerische Mathematik"},{"issue":"2","key":"856_CR2","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/BF00935547","volume":"33","author":"DQ MayneE","year":"1981","unstructured":"MayneE DQ, Heunis PJ (1981) Solving Nonlinear Inequalities in a Finite Number of Iterations. Journal of Optimization Theory and Applications 33(2):207\u2013221","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"2","key":"856_CR3","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/BF01390421","volume":"46","author":"M Sahba","year":"1985","unstructured":"Sahba M (1985) On the solution of nonlinear inequalities in a finite number of iterations. Numerische Mathematik 46(2):229\u2013236","journal-title":"Numerische Mathematik"},{"issue":"1","key":"856_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/BF01592244","volume":"71","author":"CH Chen","year":"1995","unstructured":"Chen CH, Mangasarian OL (1995) Smoothing methods for convex inequalities and linear complementarity problems. Mathematical Programming 71(1):51\u201369","journal-title":"Mathematical Programming"},{"issue":"1\u20132","key":"856_CR5","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/j.cam.2007.08.024","volume":"220","author":"ZH Huang","year":"2008","unstructured":"Huang ZH, Zhang Y, Wu W (2008) A smoothing-type algorithm for solving system of inequalities. Journal of Computational and Applied Mathematics 220(1\u20132):355\u2013363","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"9","key":"856_CR6","doi-asserted-by":"publisher","first-page":"2312","DOI":"10.1016\/j.cam.2009.10.016","volume":"233","author":"Y Zhang","year":"2010","unstructured":"Zhang Y, Huang ZH (2010) A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities. Journal of Computational and Applied Mathematics 233(9):2312\u20132321","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"10","key":"856_CR7","doi-asserted-by":"publisher","first-page":"3056","DOI":"10.1016\/j.amc.2010.04.025","volume":"216","author":"C He","year":"2010","unstructured":"He C, Ma CF (2010) A smoothing self-adaptive Levenberg Marquardt algorithm for solving system of nonlinear inequalities. Applied Mathematics and Computation 216(10):3056\u20133063","journal-title":"Applied Mathematics and Computation"},{"issue":"1","key":"856_CR8","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.amc.2008.08.039","volume":"206","author":"CF Ma","year":"2008","unstructured":"Ma CF (2008) A globally convergent Levenberg Marquardt method for the least l2-norm solution of nonlinear inequalities. Applied Mathematics and Computation 206(1):133\u2013140","journal-title":"Applied Mathematics and Computation"},{"key":"856_CR9","first-page":"1","volume":"2014","author":"JG Zhu","year":"2014","unstructured":"Zhu JG, Hao BB (2014) A New Noninterior Continuation Method for Solving a System of Equalities and Inequalities. Journal of Applied Mathematics 2014:1\u20136","journal-title":"Journal of Applied Mathematics"},{"key":"856_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s101079900127","volume":"87","author":"LQ Qi","year":"2000","unstructured":"Qi LQ, Sun DF, Zhou GL (2000) A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Mathematical Programming 87:1\u201335","journal-title":"Mathematical Programming"},{"key":"856_CR11","first-page":"1","volume":"2015","author":"Z Saeidian","year":"2015","unstructured":"Saeidian Z, Peyghami MR, Habibi M, Ghasemi S (2015) A new trust-region method for solving systems of equalities and inequalities. Computational and Applied Mathematics 2015:1\u201322","journal-title":"Computational and Applied Mathematics"},{"issue":"2","key":"856_CR12","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1023\/A:1013653923062","volume":"112","author":"YH Dai","year":"2002","unstructured":"Dai YH (2002) On the Nonmonotone Line Search. Journal of Optimization Theory and Applications 112(2):315\u2013330","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"4","key":"856_CR13","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L Grippo","year":"1986","unstructured":"Grippo L, Lampariello F, Lucidi S (1986) A Nonmonotone Line Search Technique for Newton\u2019s Method. SIAM Journal on Numerical Analysis 23(4):707\u2013716","journal-title":"SIAM Journal on Numerical Analysis"},{"issue":"3","key":"856_CR14","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/BF00940345","volume":"60","author":"L Grippo","year":"1989","unstructured":"Grippo L, Lampariello F, Lucidi S (1989) A truncated Newton method with nonmonotone line search for unconstrained optimization. Journal of Optimization Theory and Applications 60(3):401\u2013419","journal-title":"Journal of Optimization Theory and Applications"},{"key":"856_CR15","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1007\/s10915-009-9314-0","volume":"42","author":"SL Hu","year":"2010","unstructured":"Hu SL, Huang ZH, Lu N (2010) A Non-monotone Line Search Algorithm for Unconstrained Optimization. Journal of Scientific Computing 42:38\u201353","journal-title":"Journal of Scientific Computing"},{"issue":"4","key":"856_CR16","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s11075-014-9866-4","volume":"68","author":"S Huang","year":"2015","unstructured":"Huang S, Wan Z, Chen XH (2015) A new nonmonotone line search technique for unconstrained optimization. Numerical Algorithms 68(4):671\u2013689","journal-title":"Numerical Algorithms"},{"issue":"4","key":"856_CR17","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"HC Zhang","year":"2004","unstructured":"Zhang HC, Hager WW (2004) A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization. SIAM Journal on Optimizatio 14(4):1043\u20131056","journal-title":"SIAM Journal on Optimizatio"},{"issue":"1","key":"856_CR18","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1016\/j.cam.2007.07.008","volume":"219","author":"ZS Yu","year":"2008","unstructured":"Yu ZS, Pu DG (2008) A new nonmonotone line search technique for unconstrained optimization. Journal of Computational and Applied Mathematics 219(1):134\u2013144","journal-title":"Journal of Computational and Applied Mathematics"},{"issue":"3","key":"856_CR19","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1080\/10556780902769862","volume":"24","author":"SL Hu","year":"2009","unstructured":"Hu SL, Huang ZH, Wang P (2009) A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems. Optimization Methods and Softwar 24(3):447\u2013460","journal-title":"Optimization Methods and Softwar"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0856-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-0856-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0856-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T23:20:48Z","timestamp":1587511248000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-0856-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,23]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["856"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-0856-y","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,23]]},"assertion":[{"value":"27 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 February 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"91"}}