{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:02:02Z","timestamp":1761393722784},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,9,20]],"date-time":"2008-09-20T00:00:00Z","timestamp":1221868800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2010,9]]},"DOI":"10.1007\/s10589-008-9208-3","type":"journal-article","created":{"date-parts":[[2008,9,19]],"date-time":"2008-09-19T16:13:56Z","timestamp":1221840836000},"page":"33-59","source":"Crossref","is-referenced-by-count":16,"title":["Extended duality for nonlinear programming"],"prefix":"10.1007","volume":"47","author":[{"given":"Yixin","family":"Chen","sequence":"first","affiliation":[]},{"given":"Minmin","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,9,20]]},"reference":[{"key":"9208_CR1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1287\/moor.1.3.225","volume":"1","author":"J.P. Aubin","year":"1976","unstructured":"Aubin, J.P., Ekeland, I.: Estimates of the duality gap in nonconvex optimization. Math. Oper. Res. 1, 225\u2013245 (1976)","journal-title":"Math. Oper. Res."},{"key":"9208_CR2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01582066","volume":"63","author":"A. Ben-Tal","year":"1994","unstructured":"Ben-Tal, A., Eiger, G., Gershovitz, V.: Global optimization by reducing the duality gap. Math. Program. 63, 193\u2013212 (1994)","journal-title":"Math. Program."},{"issue":"3","key":"9208_CR3","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/TAC.1982.1102980","volume":"AC-27","author":"D.P. Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Distributed dynamic programming. Trans. Autom. Control AC-27(3), 610\u2013616 (1982)","journal-title":"Trans. Autom. Control"},{"key":"9208_CR4","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont (1999)"},{"issue":"1","key":"9208_CR5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.3934\/jimo.2005.1.33","volume":"1","author":"R.S. Burachik","year":"2005","unstructured":"Burachik, R.S., Rubinov, A.: On the absence of duality gap for Lagrange-type functions. J. Indust. Manag. Optim. 1(1), 33\u201338 (2005)","journal-title":"J. Indust. Manag. Optim."},{"key":"9208_CR6","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1137\/0329027","volume":"29","author":"J.V. Burke","year":"1991","unstructured":"Burke, J.V.: Calmness and exact penalization. SIAM J. Control Optim. 29, 493\u2013497 (1991)","journal-title":"SIAM J. Control Optim."},{"key":"9208_CR7","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1137\/0329054","volume":"29","author":"J.V. Burke","year":"1991","unstructured":"Burke, J.V.: An exact penalization viewpoint of constrained optimization. SIAM J. Control Optim. 29, 968\u2013998 (1991)","journal-title":"SIAM J. Control Optim."},{"key":"9208_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12211-2","volume-title":"LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization","author":"A.R. Conn","year":"1992","unstructured":"Conn, A.R., Gould, N.I.M., Toint, Ph.L.: LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization. Heidelberg, Springer (1992)"},{"key":"9208_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-53032-0","volume-title":"A Collection of Test Problems for Constrained Global Optimization Algorithms","author":"C.A. Floudas","year":"1990","unstructured":"Floudas, C.A., Pardalos, P.M.: A Collection of Test Problems for Constrained Global Optimization Algorithms. Lecture Notes in Computer Science, vol.\u00a0455. Springer, Berlin (1990)"},{"key":"9208_CR10","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1137\/S1052623499350013","volume":"12","author":"P.E. Gill","year":"2002","unstructured":"Gill, P.E., Murray, W., Saunders, M.: SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12, 979\u20131006 (2002)","journal-title":"SIAM J. Optim."},{"key":"9208_CR11","unstructured":"Gould, N.I.M., Orban, D., Toint, P.L.: An interior-point \u2113 1-penalty method for nonlinear optimization. Technical Report RAL-TR-2003-022, Rutherford Appleton Laboratory Chilton, Oxfordshire, UK, November (2003)"},{"issue":"3","key":"9208_CR12","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1287\/moor.28.3.533.16395","volume":"28","author":"X.X. Huang","year":"2003","unstructured":"Huang, X.X., Yang, X.Q.: A unified augmented Lagrangian approach to duality and exact penalization. Math. Oper. Res. 28(3), 533\u2013552 (2003)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"9208_CR13","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1162\/evco.1999.7.1.19","volume":"7","author":"S. Koziel","year":"1999","unstructured":"Koziel, S., Michalewics, Z.: Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolut. Comput. 7(1), 19\u201344 (1999)","journal-title":"Evolut. Comput."},{"key":"9208_CR14","doi-asserted-by":"crossref","unstructured":"Luo, Z.Q., Pang, J.S.: Error bounds in mathematical programming. Math. Program. Ser. B, 88(2) (2000)","DOI":"10.1007\/s101070050020"},{"issue":"4","key":"9208_CR15","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s10898-006-9122-0","volume":"40","author":"A. Nedi\u0107","year":"2008","unstructured":"Nedi\u0107, A., Ozdaglar, A.: A geometric framework for nonconvex optimization duality using augmented Lagrangian functions. J. Glob. Optim. 40(4), 545\u2013573 (2008)","journal-title":"J. Glob. Optim."},{"key":"9208_CR16","first-page":"299","volume":"79","author":"J.S. Pang","year":"1997","unstructured":"Pang, J.S.: Error bounds in mathematical programming. Math. Program. 79, 299\u2013332 (1997)","journal-title":"Math. Program."},{"key":"9208_CR17","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"R.T. Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented Lagrangian multiplier functions and duality in nonconvex programming. SIAM J. Control Optim. 12, 268\u2013285 (1974)","journal-title":"SIAM J. Control Optim."},{"key":"9208_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)"},{"key":"9208_CR19","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1137\/S1052623497326095","volume":"10","author":"A.M. Rubinov","year":"1999","unstructured":"Rubinov, A.M., Glover, B.M., Yang, X.Q.: Decreasing functions with applications to penalization. SIAM J. Optim. 10, 289\u2013313 (1999)","journal-title":"SIAM J. Optim."},{"key":"9208_CR20","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/02331939908844460","volume":"46","author":"A.M. Rubinov","year":"1999","unstructured":"Rubinov, A.M., Glover, B.M., Yang, X.Q.: Modified Lagrangian and penalty functions in continuous optimization. Optimization 46, 327\u2013351 (1999)","journal-title":"Optimization"},{"key":"9208_CR21","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10898-004-1947-9","volume":"32","author":"H. Tuy","year":"2005","unstructured":"Tuy, H.: On solving nonconvex optimization problems by reducing the duality gap. J. Glob. Optim. 32, 349\u2013365 (2005)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"9208_CR22","first-page":"65","volume":"60","author":"G.D. Ferrier","year":"1994","unstructured":"Ferrier, G.D., Goffe, W.L., Rogers, J.: Global optimization of statistical functions with simulated annealing. J. Econ. 60(1), 65\u201399 (1994)","journal-title":"J. Econ."},{"key":"9208_CR23","doi-asserted-by":"crossref","unstructured":"Wang, X., Xing, G., Zhang, Y., Lu, C., Pless, R., Gill, C.: Integrated coverage and connectivity configura-tion in wireless sensor networks. In: Proc. First ACM Conference on Embedded Networked Sensor Systems (2003)","DOI":"10.1145\/958491.958496"},{"key":"9208_CR24","doi-asserted-by":"crossref","unstructured":"Xing, G., Lu, C., Pless, R., Huang, Q.: On greedy geographic routing algorithms in sensing-covered networks. In: Proc. ACM International Symposium on Mobile Ad Hoc Networking and Computing (2004)","DOI":"10.1145\/989459.989465"},{"key":"9208_CR25","doi-asserted-by":"crossref","unstructured":"Xing, G., Lu, C., Pless, R., O\u2019Sullivan, J.A.: Co-Grid: An efficient coverage maintenance protocol for distributed sensor networks. In: Proc. International Symposium on Information Processing in Sensor Networks (2004)","DOI":"10.1145\/984622.984683"},{"key":"9208_CR26","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1137\/S1052623400371806","volume":"11","author":"X.Q. Yang","year":"2001","unstructured":"Yang, X.Q., Huang, X.X.: A nonlinear Lagrangian approach to constraint optimization problems. SIAM J. Optim. 11, 1119\u20131144 (2001)","journal-title":"SIAM J. Optim."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9208-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-008-9208-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9208-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:35Z","timestamp":1559302595000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-008-9208-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,20]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["9208"],"URL":"https:\/\/doi.org\/10.1007\/s10589-008-9208-3","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,20]]}}}