{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:32:04Z","timestamp":1672360324353},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,4,29]],"date-time":"2012-04-29T00:00:00Z","timestamp":1335657600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2013,3]]},"DOI":"10.1007\/s10898-012-9908-1","type":"journal-article","created":{"date-parts":[[2012,4,28]],"date-time":"2012-04-28T08:42:42Z","timestamp":1335602562000},"page":"559-577","source":"Crossref","is-referenced-by-count":4,"title":["A new necessary and sufficient global optimality condition for canonical DC problems"],"prefix":"10.1007","volume":"55","author":[{"given":"Qinghua","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,4,29]]},"reference":[{"key":"9908_CR1","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1057\/jors.1982.210","volume":"33","author":"M.S. Bazaraa","year":"1982","unstructured":"Bazaraa M.S., Sherali H.D.: On the use of exact and heuristic cutting plane methods for the quadratic assignment problem. J. Opl. Res. Soc. 33, 991\u20131003 (1982)","journal-title":"J. Opl. Res. Soc."},{"key":"9908_CR2","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF02283685","volume":"25","author":"S. Ben Saad","year":"1990","unstructured":"Ben Saad S., Jacobsen S.: A level set\u00a0algorithm for a class of reverse convex programs. Ann. Oper. Res. 25, 19\u201342 (1990)","journal-title":"Ann. Oper. Res."},{"key":"9908_CR3","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1515\/9781400862528.152","volume-title":"Recent Advances in Global Optimization, Princeton Series in Computer Science","author":"S. Ben Saad","year":"1991","unstructured":"Ben Saad S., Jacobsen S.: A new cutting plane algorithm for a class of reverse convex 0-1 integer programs. In: Floudas, C.A., Pardalos, P.M. (eds.) Recent Advances in Global Optimization, Princeton Series in Computer Science, pp. 152\u2013164. Princeton University Press, Princeton (1991)"},{"key":"9908_CR4","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/BF01097005","volume":"5","author":"S. Ben Saad","year":"1994","unstructured":"Ben Saad S., Jacobsen S.: Comments on a reverse convex programming algorithm. J. Global Optim. 5, 95\u201396 (1994)","journal-title":"J. Global Optim."},{"issue":"1","key":"9908_CR5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1137\/S1052623402420346","volume":"15","author":"D. Bienstock","year":"2005","unstructured":"Bienstock D., Zuckerberg M.: Subset\u00a0algebra lift operators for 0-1 integer programming. SIAM J. Optim. 15(1), 63\u201395 (2005)","journal-title":"SIAM J. Optim."},{"key":"9908_CR6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/10556780903178048","volume":"25","author":"G. Bigi","year":"2010","unstructured":"Bigi G., Frangioni A., Zhang Q.: Approximate optimality conditions and stopping criteria in canonical DC programming. Optim. Methods Softw. 25, 19\u201327 (2010)","journal-title":"Optim. Methods Softw."},{"key":"9908_CR7","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10898-009-9415-1","volume":"46","author":"G. Bigi","year":"2010","unstructured":"Bigi G., Frangioni A., Zhang Q.: Outer approximation algorithms for canonical DC problems. J. Global Optim. 46, 163\u2013189 (2010)","journal-title":"J. Global Optim."},{"key":"9908_CR8","first-page":"241","volume-title":"Handbook of Combinatorial Optimization","author":"R. Burkard","year":"1998","unstructured":"Burkard R., Cela E., Pardalos P., Pitsoulis L.: The quadratic assignment problem. In: Pardalos, P.M., Resende, M. (eds.) Handbook of Combinatorial Optimization, pp. 241\u2013337. Kluwer, Dordrecht (1998)"},{"key":"9908_CR9","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1287\/opre.41.6.1172","volume":"41","author":"M. Diaby","year":"1993","unstructured":"Diaby M.: Implicit enumeration for the pure integer 0\/1 minimax programming problem. Oper. Res. 41, 1172\u20131176 (1993)","journal-title":"Oper. Res."},{"key":"9908_CR10","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1006\/jmaa.1997.5745","volume":"217","author":"M. Dur","year":"1998","unstructured":"Dur M., Horst R., Locatelli M.: Necessary and sufficient global optimality conditions for convex maximization revisited. J. Math. Anal. Appl. 217, 637\u2013649 (1998)","journal-title":"J. Math. Anal. Appl."},{"key":"9908_CR11","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/0377-2217(90)90250-F","volume":"44","author":"J.A. Fulop","year":"1990","unstructured":"Fulop J.A.: Finite cutting plane method for solving linear programs with an additional reverse constraint. Eur. J. Oper. Res. 44, 395\u2013409 (1990)","journal-title":"Eur. J. Oper. Res."},{"key":"9908_CR12","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0167-6377(99)00074-7","volume":"26","author":"L. Grippo","year":"2000","unstructured":"Grippo L., Sciandrone M.: On the convergence of the block nonlinear gauss-seidel method under convex constraints. Oper. Res. Lett. 26, 127\u2013136 (2000)","journal-title":"Oper. Res. Lett."},{"key":"9908_CR13","doi-asserted-by":"crossref","first-page":"556","DOI":"10.2307\/2323035","volume":"93","author":"J. Hiriart-Urruty","year":"1986","unstructured":"Hiriart-Urruty J.: When is a point satisfying $${\\nabla f(x) = 0}$$ a global minimum of f?. \u00a0Am. Math. Monthly 93, 556\u2013558 (1986)","journal-title":"\u00a0Am. Math. Monthly"},{"key":"9908_CR14","volume-title":"Handbook of Global Optimization","author":"J. Hiriart-Urruty","year":"1995","unstructured":"Hiriart-Urruty J.: Conditions for global optimality. In: Horst, R., Pardalos, P.M. (eds.) Handbook of Global Optimization, Kluwer, Dordrechtr (1995)"},{"key":"9908_CR15","first-page":"55","volume":"3","author":"J. Hiriart-Urruty","year":"1996","unstructured":"Hiriart-Urruty J., Ledyaev Y.S.: A note on the characterization of the global maxima of a (tangentially) convex function over a convex set. J. Convex Anal. 3, 55\u201361 (1996)","journal-title":"J. Convex Anal."},{"key":"9908_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-0015-5","volume-title":"Introduction to Global Optimization","author":"R. Horst","year":"2000","unstructured":"Horst R., Pardalos P., Thoai N.: Introduction to Global Optimization, 2nd edn. Kluwer, Dordrecht (2000)","edition":"2"},{"key":"9908_CR17","unstructured":"Horst, R., Thoai, N.: DC programming. In: Floudas C, Pardalos P (eds) Encyclopedia of Optimization. Nonconvex Optimizational Applications. Kluwer, Dordrecht, Holland, vol. 53, pp. 375\u2013378 (2001)"},{"key":"9908_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02598-7","volume-title":"Global Optimization","author":"R. Horst","year":"1990","unstructured":"Horst R., Tuy H.: Global Optimization. Springer, Berlin (1990)"},{"key":"9908_CR19","first-page":"241","volume":"11","author":"M. Nghia","year":"1986","unstructured":"Nghia M., Hieu N.: A method for solving reverse convex programming problems. Acta Math. Vietnam. 11, 241\u2013252 (1986)","journal-title":"Acta Math. Vietnam."},{"key":"9908_CR20","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1023\/A:1008217604285","volume":"10","author":"A.D. Rikun","year":"1997","unstructured":"Rikun A.D.: A convex envelope formula for multilinear functions. J. Global Optim. 10, 425\u2013437 (1997)","journal-title":"J. Global Optim."},{"key":"9908_CR21","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1017\/S0004972700010844","volume":"20","author":"I. Singer","year":"1979","unstructured":"Singer I.: A Fenchel-Rockafellar type duality theorem for maximization. Bull. Austral. Math. Soc. 20, 193\u2013198 (1979)","journal-title":"Bull. Austral. Math. Soc."},{"key":"9908_CR22","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0022-247X(92)90385-Q","volume":"171","author":"I. Singer","year":"1992","unstructured":"Singer I.: Some further duality theorem for optimization problems with reverse convex constraint sets. J. Math. Anal. Appl. 171, 205\u2013219 (1992)","journal-title":"J. Math. Anal. Appl."},{"key":"9908_CR23","first-page":"1062","volume":"292","author":"A. Strekalovsky","year":"1987","unstructured":"Strekalovsky A.: On the global extremum problem. Soviet Dokl 292, 1062\u20131066 (1987)","journal-title":"Soviet Dokl"},{"key":"9908_CR24","first-page":"74","volume":"8","author":"A. Strekalovsky","year":"1990","unstructured":"Strekalovsky A.: On problems of global extremum in nonconvex extremal problems. Izv. Vozou. Mat. 8, 74\u201380 (1990)","journal-title":"Izv. Vozou. Mat."},{"key":"9908_CR25","first-page":"94","volume":"2","author":"A. Strekalovsky","year":"1991","unstructured":"Strekalovsky A.: On conditions for global extremum in a nonconvex minimization problem. Izv. Vozou. Mat. 2, 94\u201396 (1991)","journal-title":"Izv. Vozou. Mat."},{"key":"9908_CR26","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1008260227877","volume":"13","author":"A. Strekalovsky","year":"1998","unstructured":"Strekalovsky A., Tsevendorj I.: Testing the $${\\mathbb{R}}$$ -strategy for a reverse convex problem. J. Global Optim. 13, 61\u201374 (1998)","journal-title":"J. Global Optim."},{"key":"9908_CR27","first-page":"97","volume":"87","author":"P. Tao","year":"1989","unstructured":"Tao P., El Bernoussi S.: Numerical methods for solving a class of global nonconvex optimization problems. Int. Ser. Numer. Math. 87, 97\u2013132 (1989)","journal-title":"Int. Ser. Numer. Math."},{"key":"9908_CR28","first-page":"35","volume":"10","author":"P. Thach","year":"1985","unstructured":"Thach P.: Convex programs with several additional reverse convex constraints. Acta Math. Vietnam. 10, 35\u201357 (1985)","journal-title":"Acta Math. Vietnam."},{"key":"9908_CR29","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1080\/02331938808843381","volume":"19","author":"N. Thoai","year":"1988","unstructured":"Thoai N.: A modified version of Tuy\u2019s method for solving d.c. programming problems. Optimization 19, 665\u2013674 (1988)","journal-title":"Optimization"},{"key":"9908_CR30","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1006\/jmaa.1998.6040","volume":"225","author":"N. Thoai","year":"1998","unstructured":"Thoai N.: On Tikhonov\u2019s reciprocity principle and optimality conditions in DC optimization. J. Math. Anal. Appl. 225, 673\u2013678 (1998)","journal-title":"J. Math. Anal. Appl."},{"key":"9908_CR31","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0022-247X(78)90243-3","volume":"66","author":"J.F. Toland","year":"1978","unstructured":"Toland J.F.: Duality in nonconvex optimization. J. Math. Anal. Appl. 66, 399\u2013415 (1978)","journal-title":"J. Math. Anal. Appl."},{"key":"9908_CR32","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF00250669","volume":"71","author":"J. F. Toland","year":"1979","unstructured":"Toland J. F.: A duality principle for nonconvex optimization and the calculus of variations. Arch. Rational Mech. Anal. 71, 41\u201361 (1979)","journal-title":"Arch. Rational Mech. Anal."},{"key":"9908_CR33","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1023\/A:1008331305949","volume":"16","author":"H. Tuan","year":"2000","unstructured":"Tuan H.: Remarks on an algorithm for reverse convex programs. J. Global Optim. 16, 295\u2013297 (2000)","journal-title":"J. Global Optim."},{"key":"9908_CR34","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0304-0208(08)72403-4","volume-title":"FERMAT days 85: mathematics for optimization. North-Holland Mathematical Studies 129","author":"H. Tuy","year":"1986","unstructured":"Tuy H.: A general deterministic approach to global optimization via d.c. programming. In: Hiriart-Urruty, J. (Ed.) FERMAT days 85: mathematics for optimization. North-Holland Mathematical Studies 129, pp. 273\u2013303. North-Holland Publishing Co., Toulouse (1986)"},{"key":"9908_CR35","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BF00938217","volume":"52","author":"H. Tuy","year":"1987","unstructured":"Tuy H.: Convex programs with an additional reverse convex constraint. J. Optim. Theory Appl. 52, 463\u2013486 (1987)","journal-title":"J. Optim. Theory Appl."},{"key":"9908_CR36","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/BFb0121159","volume":"30","author":"H. Tuy","year":"1987","unstructured":"Tuy H.: Global minimization of a difference of two convex functions. Math. Program. Study 30, 150\u2013182 (1987)","journal-title":"Math. Program. Study"},{"key":"9908_CR37","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0167-6377(95)00037-X","volume":"18","author":"H. Tuy","year":"1995","unstructured":"Tuy H.: Canonical DC programming problem: outer approximation methods revisited. Oper. Res. Lett. 18, 99\u2013106 (1995)","journal-title":"Oper. Res. Lett."},{"key":"9908_CR38","first-page":"149","volume-title":"Handbook of Global Optimization, Nonconvex Optimization and Its Applications, 2","author":"H. Tuy","year":"1995","unstructured":"Tuy H.: D.C.optimization: theory, methods and algorithms. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization, Nonconvex Optimization and Its Applications, 2, pp. 149\u2013216. Kluwer, Dordrecht (1995)"},{"key":"9908_CR39","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1023\/A:1024751811328","volume":"118","author":"H. Tuy","year":"2003","unstructured":"Tuy H.: On global optimality conditions and cutting plane algorithms. J. Optim. Theory Appl. 118, 201\u2013216 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"9908_CR40","unstructured":"Zhang, Q.: Outer approximation algorithms for DC programs and beyond. Ph.D. thesis. University of Pisa, Pisa, Italy (2008)"},{"key":"9908_CR41","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10288-010-0126-8","volume":"8","author":"Q. Zhang","year":"2010","unstructured":"Zhang Q.: Outer approximation algorithms for DC programs and beyond. 4OR-Q J. Oper. Res. 8, 323\u2013326 (2010)","journal-title":"4OR-Q J. Oper. Res."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9908-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-012-9908-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-012-9908-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T01:45:55Z","timestamp":1561686355000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-012-9908-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,29]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["9908"],"URL":"https:\/\/doi.org\/10.1007\/s10898-012-9908-1","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,29]]}}}