{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:10:34Z","timestamp":1751429434236,"version":"3.41.0"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,1,1]],"date-time":"2002-01-01T00:00:00Z","timestamp":1009843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Global Optimization"],"published-print":{"date-parts":[[2002,1]]},"DOI":"10.1023\/a:1013871532570","type":"journal-article","created":{"date-parts":[[2002,12,28]],"date-time":"2002-12-28T18:50:27Z","timestamp":1041101427000},"page":"263-270","source":"Crossref","is-referenced-by-count":6,"title":["Convergence of duality bound method in partly convex programming"],"prefix":"10.1007","volume":"22","author":[{"given":"Nguyen Van","family":"Thoai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"383105_CR1","doi-asserted-by":"crossref","unstructured":"Bank, B., Guddat, J., Klatte, D., Kummer, B. and Tammer, K. (1983), Nonlinear Parametric Optimization. Birkhaeuser,Basel.","DOI":"10.1007\/978-3-0348-6328-5"},{"key":"383105_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. and Gershovitz, V. (1994), GlobalMinimization by Reducing the Duality Gap. Mathematical Programming 63: 193\u2013212.","journal-title":"Mathematical Programming"},{"key":"383105_CR3","unstructured":"Duer, M. (1999), Duality in Global Optimization: Optimality Conditions and Algorithmical Aspects Ph.D. Thesis, University of Trier."},{"key":"383105_CR4","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1023\/A:1022687222060","volume":"95","author":"M. Duer","year":"1997","unstructured":"Duer, M. and Horst, R. (1997), Lagrange Duality and Partioning Techniques in Nonconvex Global Optimization. Journal of Optimization Theory and Applications 95: 347\u2013369.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"383105_CR5","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1080\/02331930108844543","volume":"49","author":"M. Duer","year":"2001","unstructured":"Duer, M., Horst, R. and Thoai, N.V. (2001), Solving Sum-of-Ratios Fractional Programs Using Efficient Points Optimization 49: 447\u2013466.","journal-title":"Optimization"},{"key":"383105_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/1013001","volume":"13","author":"A.M. Geoffrion","year":"1971","unstructured":"Geoffrion, A.M. (1971), Duality in Nonlinear Programming: A Simplified Application-Oriented Development. SIAM Review 13, 1\u201337.","journal-title":"SIAM Review"},{"key":"383105_CR7","volume-title":"Nonlinear Programming","author":"O.L. Mangasaian","year":"1979","unstructured":"Mangasaian, O.L. (1979), Nonlinear Programming. Robert E. Krieger, Huntington, New York."},{"key":"383105_CR8","series-title":"Research Report","volume-title":"Forthcoming in Journal of Optimization Theory and Applications","author":"N.V. Thoai","year":"1997","unstructured":"Thoai, N.V. (1997), On Convergence and Application of a Decomposition Method Using Duality Bounds for Nonconvex Global Optimization. Research Report Nr. 97\u201324, University of Trier, Germany. Forthcoming in Journal of Optimization Theory and Applications."},{"key":"383105_CR9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1023\/A:1026437621223","volume":"107","author":"N.V. Thoai","year":"2000","unstructured":"Thoai, N.V. (2000), Duality Bound Methods for the General Quadratic Programming Problem with Quadratic Constraints Journal of Optimization Theory and Applications 107, 331\u2013354.","journal-title":"Journal of Optimization Theory and Applications"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1013871532570.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1013871532570\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1013871532570.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:38:32Z","timestamp":1751366312000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1013871532570"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":9,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["383105"],"URL":"https:\/\/doi.org\/10.1023\/a:1013871532570","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}