{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T10:29:59Z","timestamp":1720693799718},"reference-count":0,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[1983,5]]},"abstract":" The problem of minimizing a concave function subject to linear inequality constraints may have many local solutions. Therefore, finding the global constrained minimum is a computationally difficult problem. <\/jats:p> A computational method is described which finds the global minimum of a smooth concave function over a polyhedron in Rn<\/jats:sub>. The feasible domain is partitioned into a rectangular domain, which can be excluded from further consideration, and r \u2264 2n subdomains, at least one of which contains the global minimum. A known algorithm can be applied sequentially (or in parallel) to each of these r subdomains to compute the global minimum. <\/jats:p> A method is also presented (Appendix B) for the construction of nontrivial test problems for which the global minimum point is known. Given an arbitrary polyhedron and a selected vertex, it is shown how to determine a concave quadratic function (generally with many local minima) with its global minimum at the selected vertex. <\/jats:p>","DOI":"10.1287\/moor.8.2.215","type":"journal-article","created":{"date-parts":[[2008,10,31]],"date-time":"2008-10-31T22:43:38Z","timestamp":1225493018000},"page":"215-230","source":"Crossref","is-referenced-by-count":60,"title":["Global Minimization of a Linearly Constrained Concave Function by Partition of Feasible Domain"],"prefix":"10.1287","volume":"8","author":[{"given":"J. B.","family":"Rosen","sequence":"first","affiliation":[{"name":"Computer Science Department, University of Minnesota, Minneapolis, Minnesota 55455"}]}],"member":"109","container-title":["Mathematics of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/moor.8.2.215","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T10:58:36Z","timestamp":1680433116000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/moor.8.2.215"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,5]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1983,5]]}},"alternative-id":["10.1287\/moor.8.2.215"],"URL":"https:\/\/doi.org\/10.1287\/moor.8.2.215","relation":{},"ISSN":["0364-765X","1526-5471"],"issn-type":[{"value":"0364-765X","type":"print"},{"value":"1526-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,5]]}}}