{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:25:34Z","timestamp":1759847134485,"version":"3.33.0"},"reference-count":23,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4058,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An exponential potential\u2010function reduction algorithm for convex block\u2010angular optimization problems is described. These problems are characterized by<jats:italic>K<\/jats:italic>disjoint convex compact sets called blocks and<jats:italic>M<\/jats:italic>non\u2010negative\u2010valued convex block\u2010separable coupling inequalities with a nonempty interior. A given convex block\u2010separable function is to be minimized. Concurrent, minimum\u2010cost, and generalized multicommodity network flow problems are important special cases of this model. The method reduces the optimization problem to two resource\u2010sharing problems. The first of these problems is solved to obtain a feasible solution interior to the coupling constraints. Starting from this solution, The algorithm proceeds to solve the second problem on the original constraints, but with a modified exponential potential function. The method is shown to produce an \u03f5\u2010approximate solution in<jats:italic>O<\/jats:italic>(<jats:italic>K<\/jats:italic>(In<jats:italic>M<\/jats:italic>)(\u03f5<jats:sup>\u22122<\/jats:sup>+ in<jats:italic>K<\/jats:italic>)) iterations, provided that there is a feasible solution sufficiently interior to the coupling inequalities. Each iteration consists of solving a subset of independent block problems, followed by a simple coordination step. Computational experiments with a set of large linear concurrent and minimum\u2010cost multicommodity network flow problems suggest that the method can be practical for computing fast approximations to large instances.<\/jats:p>","DOI":"10.1002\/net.3230260202","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T20:17:47Z","timestamp":1179001067000},"page":"59-68","source":"Crossref","is-referenced-by-count":23,"title":["An exponential\u2010function reduction method for block\u2010angular convex programs"],"prefix":"10.1002","volume":"26","author":[{"given":"Michael D.","family":"Grigoriadis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonid G.","family":"Khachiyan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.38.2.240"},{"key":"e_1_2_1_3_2","first-page":"58","volume-title":"Proceedings of the SIAM Workshop on Large\u2010Scale Numerical Optimization","author":"Choi I. C.","year":"1990"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/1911818"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0121089"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0804004"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584987"},{"volume-title":"IBM Optimization Subroutine Library (OSL)\u2014Guide and Reference","year":"1991","series-title":"Release 2. Publication SC23\u20100519\u201002","key":"e_1_2_1_8_2"},{"key":"e_1_2_1_9_2","unstructured":"P. N.Klein S.KangandJ.Borger Approximating concurrent flow with uniform demands and capacities: An implementation. Technical Report 92\u20104 DIMACS Implementation Challenge Workshop (D. S. Johnson and C. C. McGeoch Eds.) (1992)225\u2013240."},{"volume-title":"Optimization Theory for Large Systems","year":"1970","author":"Lasdon L. S.","key":"e_1_2_1_10_2"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1995.1020"},{"key":"e_1_2_1_12_2","unstructured":"T.Leong P.ShorandC.Stein Implementation of a combinatorial multicommodity flow algorithm. Technical Report 92\u20104 DIMACS Implementation Challenge Workshop (D. S. Johnson and C. C. McGeoch Eds.) (1992)202\u2013224."},{"volume-title":"Nonlinear Programming","year":"1969","author":"Mangasarian O. L.","key":"e_1_2_1_13_2"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1287\/inte.20.4.105"},{"volume-title":"Nonlinear Programming\u2014Theory and Algorithms","year":"1983","author":"McCormick G. P.","key":"e_1_2_1_15_2"},{"volume-title":"Project SCOOP Symp. on Linear Inequalities and Programming","year":"1952","author":"Motzkin T. S.","key":"e_1_2_1_16_2"},{"key":"e_1_2_1_17_2","unstructured":"B. A.Murtagh andM. A.Saunders MINOS 5.4 User's Guide. Technical Report SOL\u201083\u201020R. Department of Operations Research Stanford University Stanford CA (December 1983) (Rev. March1993)."},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/0721052"},{"key":"e_1_2_1_19_2","doi-asserted-by":"crossref","unstructured":"S.Plotkin D. B.ShmoysandE.Tardos Fast approximation algorithms for fractional packing and covering problems. Proceedings of the 32nd Annual Symposium on Foundations of Computer Science (1991)495\u2013504.","DOI":"10.1109\/SFCS.1991.185411"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.4.3.235"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386073"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1137\/0801035"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1.2.62"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1145\/77600.77620"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230260202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230260202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T05:55:59Z","timestamp":1737006959000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230260202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1002\/net.3230260202"],"URL":"https:\/\/doi.org\/10.1002\/net.3230260202","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"type":"print","value":"0028-3045"},{"type":"electronic","value":"1097-0037"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}