{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:37:00Z","timestamp":1774265820033,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T00:00:00Z","timestamp":1149638400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Applic"],"published-print":{"date-parts":[[2006,11]]},"DOI":"10.1007\/s10589-006-8720-6","type":"journal-article","created":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T10:42:21Z","timestamp":1149676941000},"page":"375-398","source":"Crossref","is-referenced-by-count":34,"title":["On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization"],"prefix":"10.1007","volume":"35","author":[{"given":"Zhiqing","family":"Meng","sequence":"first","affiliation":[]},{"given":"Chuangyin","family":"Dang","sequence":"additional","affiliation":[]},{"given":"Xiaoqi","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,6,7]]},"reference":[{"key":"8720_CR1","first-page":"334","volume":"13","author":"W.I. Zangwill","year":"1967","unstructured":"W.I. Zangwill, \u201cNonlinear programming via penalty function,\u201d Manangement Science, vol. 13, pp. 334\u2013358, 1967.","journal-title":"Manangement Science"},{"key":"8720_CR2","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF01588250","volume":"17","author":"S.P. Han","year":"1979","unstructured":"S.P. Han and O.L. Mangasrian, \u201cExact penalty function in nonlinear programming,\u201d Mathematical Programming, vol. 17, pp. 251\u2013269, 1979.","journal-title":"Mathematical Programming"},{"key":"8720_CR3","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1287\/moor.6.3.437","volume":"6","author":"E. Rosenberg","year":"1981","unstructured":"E. Rosenberg, \u201cGlobally convergent algorithms for convex programming,\u201d Mathematics of Operational Rresearch, vol. 6, pp. 437\u2013443, 1981.","journal-title":"Mathematics of Operational Rresearch"},{"key":"8720_CR4","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0377-2217(81)90097-7","volume":"7","author":"J.B. Lasserre","year":"1981","unstructured":"J.B. Lasserre, \u201cA globally convergent algorithm for exact penalty functions,\u201d European Journal of Opterational Research, vol. 7, pp. 389\u2013395, 1981.","journal-title":"European Journal of Opterational Research"},{"key":"8720_CR5","volume-title":"Optimization and Nonsmooth Analysis","author":"F.H. Clarke","year":"1982","unstructured":"F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1982."},{"key":"8720_CR6","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/BF02591938","volume":"30","author":"E. Rosenberg","year":"1984","unstructured":"E. Rosenberg, \u201cExact penalty functions and stability in locally Lipschitz programming,\u201d Mathematical Programming, vol. 30, pp. 340\u2013356, 1984.","journal-title":"Mathematical Programming"},{"key":"8720_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02591986","volume":"36","author":"G. Di Pillo","year":"1986","unstructured":"G. Di Pillo and L. Grippo, \u201cAn exact penalty function method with global conergence properties for nonlinear programming problems,\u201d Mathemathical Programming, vol. 36, pp. 1\u201318, 1986.","journal-title":"Mathemathical Programming"},{"key":"8720_CR8","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/BF02346160","volume":"57","author":"G. Di Pillo","year":"1988","unstructured":"G. Di Pillo and L. Grippo, \u201cOn the exactness of a class of nondifferentiable penalty function,\u201d Journal of Optimization Theory and Applications, vol. 57, pp. 385\u2013406, 1988.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"8720_CR9","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/0377-2217(93)90181-L","volume":"64","author":"S.A. Zenios","year":"1993","unstructured":"S.A. Zenios, M.C. Pinar, and R.S. Dembo, \u201cA smooth penalty function algorithm for network-structured problems,\u201d European Journal of Operational Research, vol. 64, pp. 258\u2013277, 1993.","journal-title":"European Journal of Operational Research"},{"key":"8720_CR10","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1137\/0804027","volume":"4","author":"M.C. Pinar","year":"1994","unstructured":"M.C. Pinar and S.A. Zenios, \u201cOn smoothing exact penalty functions for convex constarained optimization,\u201d SIAM Journal on Optimization, vol. 4, pp. 486\u2013511, 1994.","journal-title":"SIAM Journal on Optimization"},{"key":"8720_CR11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01592244","volume":"71","author":"C. Chen","year":"1995","unstructured":"C. Chen and O.L. Mangasarian, \u201cSmoothing methods for convex inequalities and linear complementarity problems,\u201d Mathematical Programming, vol. 71, pp. 51\u201369, 1995.","journal-title":"Mathematical Programming"},{"key":"8720_CR12","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1081\/NFA-120022928","volume":"24","author":"X.Q. Yang","year":"2003","unstructured":"X.Q. Yang, Z.Q. Meng, X.X. Huang, and G.T.Y. Pong, \u201cSmoothing nonlinear penalty functions for constrained optimization,\u201d Numerical Functional Analysis and Optimization, vol. 24, pp. 351\u2013364, 2003.","journal-title":"Numerical Functional Analysis and Optimization"},{"key":"8720_CR13","doi-asserted-by":"crossref","unstructured":"S.C. Fang, J.R. Rajasekera, and H.S.J. Tsao, Entropy Optimization and Mathematical Proggramming, Kluwer, 1997.","DOI":"10.1007\/978-1-4615-6131-6"},{"key":"8720_CR14","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1023\/A:1024814401713","volume":"27","author":"L. Qi","year":"2003","unstructured":"L. Qi, S.Y. Wu, and G. Zhou, \u201cSemismooth newton methods for solving semi-infinite programming problems,\u201d Journal of Global Optimization, vol. 27, pp. 215\u2013232, 2003.","journal-title":"Journal of Global Optimization"},{"key":"8720_CR15","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1023\/A:1019260508329","volume":"98","author":"K.L. Teo","year":"2000","unstructured":"K.L. Teo, X.Q. Yang, and L.S. Jennings, \u201cComputational discretization algorithms for functional inequality constrained optimization,\u201d Annals of Operations Research, vol. 98, pp. 215\u2013234, 2000.","journal-title":"Annals of Operations Research"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-8720-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-006-8720-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-8720-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:30Z","timestamp":1559302590000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-006-8720-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6,7]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,11]]}},"alternative-id":["8720"],"URL":"https:\/\/doi.org\/10.1007\/s10589-006-8720-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6,7]]}}}