{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:20Z","timestamp":1740134540613,"version":"3.37.3"},"reference-count":33,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["70771030","70271047","11261010","2012RCYJ005"],"award-info":[{"award-number":["70771030","70271047","11261010","2012RCYJ005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["70771030","70271047","11261010","2012RCYJ005"],"award-info":[{"award-number":["70771030","70271047","11261010","2012RCYJ005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["70771030","70271047","11261010","2012RCYJ005"],"award-info":[{"award-number":["70771030","70271047","11261010","2012RCYJ005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project Science Foundation of Guangdong University of Finance","award":["70771030","70271047","11261010","2012RCYJ005"],"award-info":[{"award-number":["70771030","70271047","11261010","2012RCYJ005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducing<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>auxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian duality theory. The proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. Some examples are given to illustrate the feasibility of the present algorithm.<\/jats:p>","DOI":"10.1155\/2013\/984168","type":"journal-article","created":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T17:03:26Z","timestamp":1365440606000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xue-Gang","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing-Yuan","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00121658"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9323-9"},{"volume":"22","year":"1998","key":"3"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0000035"},{"first-page":"217","volume-title":"Quadratic optimization","year":"1995","key":"5"},{"volume":"3","year":"1995","key":"6"},{"volume":"15","year":"1997","key":"9"},{"key":"10","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1137\/0112064","volume":"12","year":"1964","journal-title":"Journal of the Society for Industrial and Applied Mathematics"},{"issue":"1","key":"11","first-page":"376","volume":"7","year":"1979","journal-title":"Mathematical Programming"},{"key":"12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF01580119","volume":"5","year":"1973","journal-title":"Mathematical Programming"},{"key":"13","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1287\/opre.17.4.680","volume":"17","year":"1969","journal-title":"Operations Research"},{"year":"1998","key":"14"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01096534"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00120666"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/BF00130830"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02283691"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01096774"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024700901538"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021725517203"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008316429329"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1287\/opre.43.2.264"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.074"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.03.031"},{"key":"26","first-page":"156","volume":"26","year":"1994","journal-title":"Computing Sciences AndStatistics"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1080\/02331939008843615"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01096535"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192573"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004657629105"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022600232285"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008308913266"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-005-2655-4"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.08.036"},{"year":"1993","key":"35"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/984168.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/984168.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/984168.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T07:01:49Z","timestamp":1498028509000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/984168\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":33,"alternative-id":["984168","984168"],"URL":"https:\/\/doi.org\/10.1155\/2013\/984168","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}