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Firstly, by introducing new variables and constraints, we transform the original problem into an equivalent nonconvex programs problem. Secondly, by utilizing new linear relaxation technique, we establish the linear relaxation programs problem of the equivalent problem. Thirdly, based on the out space partition and the linear relaxation programs problem, we construct an out space branch-and-bound algorithm. Fourthly, to improve the computational efficiency of the algorithm, an out space reduction operation is employed as an accelerating device for deleting a large part of the investigated out space region. Finally, the global convergence of the algorithm is proved, and numerical results demonstrate the feasibility and effectiveness of the proposed algorithm.<\/jats:p>","DOI":"10.1155\/2017\/5249160","type":"journal-article","created":{"date-parts":[[2017,6,14]],"date-time":"2017-06-14T17:04:21Z","timestamp":1497459861000},"page":"1-7","source":"Crossref","is-referenced-by-count":2,"title":["An Out Space Accelerating Algorithm for Generalized Affine Multiplicative Programs Problem"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4811-5854","authenticated-orcid":true,"given":"Lei","family":"Cai","sequence":"first","affiliation":[{"name":"School of Information Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1800-6016","authenticated-orcid":true,"given":"Shuai","family":"Tang","sequence":"additional","affiliation":[{"name":"Jiyuan Vocational and Technical College, Jiyuan 459000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0968-9142","authenticated-orcid":true,"given":"Jingben","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4815-6453","authenticated-orcid":true,"given":"Zhisong","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3695-387X","authenticated-orcid":true,"given":"Hongwei","family":"Jiao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4098-4"},{"year":"1971","key":"2"},{"key":"3","first-page":"223","volume":"8","year":"1966","journal-title":"Cahier du Coutre d\u2019Etudes de Recherche Operationelle"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.04.076"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.08.015"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.12.007"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.02.159"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.12.039"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008314922240"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024700901538"},{"issue":"5","key":"11","first-page":"13","volume":"36","year":"2008","journal-title":"Journal of Henan Normal University (Natural Science)"},{"issue":"4","key":"12","first-page":"391","volume":"31","year":"2003","journal-title":"Vietnam Journal of Mathematics"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192573"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-012-0576-6"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004657629105"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008308913266"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023274721632"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2008.11.002"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.09.002"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.03.025"}],"container-title":["Journal of Control Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jcse\/2017\/5249160.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jcse\/2017\/5249160.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jcse\/2017\/5249160.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,14]],"date-time":"2017-06-14T17:04:31Z","timestamp":1497459871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jcse\/2017\/5249160\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"references-count":20,"alternative-id":["5249160","5249160"],"URL":"https:\/\/doi.org\/10.1155\/2017\/5249160","relation":{},"ISSN":["1687-5249","1687-5257"],"issn-type":[{"type":"print","value":"1687-5249"},{"type":"electronic","value":"1687-5257"}],"subject":[],"published":{"date-parts":[[2017]]}}}