{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:26:01Z","timestamp":1773239161708,"version":"3.50.1"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,5,17]],"date-time":"2006-05-17T00:00:00Z","timestamp":1147824000000},"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":[[2006,9]]},"DOI":"10.1007\/s10589-006-6441-5","type":"journal-article","created":{"date-parts":[[2006,5,17]],"date-time":"2006-05-17T16:49:20Z","timestamp":1147884560000},"page":"47-67","source":"Crossref","is-referenced-by-count":18,"title":["Calmness and Exact Penalization in Vector Optimization with Cone Constraints"],"prefix":"10.1007","volume":"35","author":[{"given":"X.","family":"X. Huang","sequence":"first","affiliation":[]},{"given":"K. L.","family":"Teo","sequence":"additional","affiliation":[]},{"given":"X. Q.","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,5,17]]},"reference":[{"key":"6441_CR1","doi-asserted-by":"crossref","unstructured":"J.V. Burke, \u201cCalmness and Exact Penalization,\u201d SIAM Journal on Control and Optimization, pp. 493\u2013497, 1991.","DOI":"10.1137\/0329027"},{"key":"6441_CR2","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1137\/0329054","volume":"29","author":"J.V. Burke","year":"1991","unstructured":"J.V. Burke, \u201cAn exact penalization viewpoint of constrained optimization,\u201d SIAM Journal on Control and Optimization, vol. 29, pp. 968\u2013998, 1991.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"6441_CR3","volume-title":"Optimization and Nonsmooth Analysis","author":"F.H. Clarke","year":"1983","unstructured":"F.H. Clarke, Optimization and Nonsmooth Analysis, John-Wiley & Sons: New York, 1983."},{"key":"6441_CR4","volume-title":"Nonlinear Programming: Sequential Unconstrained Minimization Techniques","author":"A. Fiacco","year":"1968","unstructured":"A. Fiacco and G. McCormic, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John-Wiley & Sons: New York, 1968."},{"key":"6441_CR5","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"R. Fletcher, Practical Methods of Optimization, John-Wiley & Sons: New York, 1987."},{"key":"6441_CR6","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/02331930290019440","volume":"51","author":"X.X. Huang","year":"2003","unstructured":"X.X. Huang, \u201cOptimality conditions and approximate optimality conditions for locally Lipschitz vector optimization,\u201d Optimization, vol. 51, pp. 309\u2013321, 2003.","journal-title":"Optimization"},{"key":"6441_CR7","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1287\/moor.28.3.533.16395","volume":"28","author":"X.X. Huang","year":"2003","unstructured":"X.X. Huang and X.Q. Yang, \u201cA unified augmented Lagrangian approach to duality and exact penalization,\u201d Mathematics of Operations Research, vol. 28, pp. 533\u2013552, 2003.","journal-title":"Mathematics of Operations Research"},{"key":"6441_CR8","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1137\/S1052623401384850","volume":"13","author":"X.X. Huang","year":"2002","unstructured":"X.X. Huang and X.Q. Yang, \u201cNonlinear Lagrangian for multiobjective optimization problems and applications to duality and exact penalization,\u201d SIAM J. Optim., vol. 13, pp. 675\u2013692, 2002.","journal-title":"SIAM J. Optim."},{"key":"6441_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-50280-4","volume-title":"Theory of Vector Optimization","author":"D.T. Luc","year":"1989","unstructured":"D.T. Luc, Theory of Vector Optimization, Springer-Verlag: Berlin, 1989."},{"key":"6441_CR10","doi-asserted-by":"crossref","unstructured":"Z.Q. Luo, J.S. Pang, and D. Ralph, Mathematical Programs with Equilibrium Constraints, Cambridge University Press, 1997.","DOI":"10.1017\/CBO9780511983658"},{"key":"6441_CR11","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":"6441_CR12","first-page":"148","volume":"12","author":"G. Z. Ruan","year":"1992","unstructured":"G.Z. Ruan and X.X. Huang, \u201cWeak calmness and weak stability of multiobjective programming and its penalty functions,\u201d Systems Science and Mathematical Sciences, vol. 12, pp. 148\u2013157, 1992 (in Chinese).","journal-title":"Systems Science and Mathematical Sciences"},{"key":"6441_CR13","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1137\/S1052623497326095","volume":"10","author":"A.M. Rubinov","year":"1999","unstructured":"A.M. Rubinov, B.M. Glover and X.Q. Yang, \u201cDecreasing functions with applications to penalization,\u201d SIAM J. Optim., vol. 10, pp. 289\u2013313, 1999.","journal-title":"SIAM J. Optim."},{"key":"6441_CR14","doi-asserted-by":"crossref","unstructured":"A. Rubinov and X.Q. Yang, Lagrange-Type Functions in Constrained Non-convex Optimization,\u2019 Kluwer Academic Publishers, 2003.","DOI":"10.1007\/978-1-4419-9172-0"},{"key":"6441_CR15","first-page":"301","volume":"77","author":"A. Shapiro","year":"1997","unstructured":"A. Shapiro, \u201cFirst and second order analysis of nonlinear semidefinite programs,\u201d Mathematical Programming, Ser. B, vol. 77, pp. 301\u2013320, 1997.","journal-title":"Mathematical Programming, Ser. B"},{"key":"6441_CR16","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF00935007","volume":"43","author":"D.J. White","year":"1984","unstructured":"D.J. White, \u201cMultiobjective programming and penalty functions,\u201d Journal of Optimization Theory and Applications, vol. 43, pp. 583\u2013599, 1984.","journal-title":"Journal of Optimization Theory and Applications"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-6441-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-006-6441-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-6441-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:30Z","timestamp":1559288190000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-006-6441-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,17]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,9]]}},"alternative-id":["6441"],"URL":"https:\/\/doi.org\/10.1007\/s10589-006-6441-5","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5,17]]}}}