{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T22:47:17Z","timestamp":1757544437948},"reference-count":19,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,3,9]],"date-time":"2007-03-09T00:00:00Z","timestamp":1173398400000},"content-version":"vor","delay-in-days":8590,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Previous feasible direction algorithms for convex, separable network flow problems that have appeared in the literature have all been linearly convergent. In this paper we propose an approximate implementation of the quadratically convergent Newton algorithm. The key to this implementation is a conjugate direction method that determines second\u2010order dual multiplier estimates at each iteration. This method exploits the network structure in a way that allows certain crucial matrix\u2010vector products to be computed in a simple pass through the arcs. Since this novel approach requires no matrix storage to compute these products, the algorithm can be used for large\u2010scale problems. Some computational experience with this new algorithm is reported.<\/jats:p>","DOI":"10.1002\/net.3230130310","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T16:49:51Z","timestamp":1178902191000},"page":"427-442","source":"Crossref","is-referenced-by-count":30,"title":["A Newton method for convex separable network flow problems"],"prefix":"10.1002","volume":"13","author":[{"given":"John G.","family":"Klincewicz","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,9]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"A. I.Ali R. V.Helgason andJ. L.Kennington The convex cost network flow problem: A state\u2010of\u2010the\u2010art survey. Technical Report OREM 78001 Southern Methodist University 1978.","DOI":"10.21236\/ADA051069"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230080405"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0116614"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.24.1.1"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.24.7.747"},{"key":"e_1_2_1_7_2","unstructured":"L.Cooper andJ. L.Kennington Steady\u2010state analysis of nonlinear resistive electrical networks using optimization techniques. Technical Report IEOR 77012 Southern Methodist University 1977."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0719025"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120941"},{"key":"e_1_2_1_10_2","first-page":"29","volume-title":"Numerical Methods for Constrained Optimization","author":"Gill P. E.","year":"1974"},{"key":"e_1_2_1_11_2","unstructured":"P. E.GillandW.Murray Safeguarded step\u2013length algorithms for optimization using descent methods. Report NAC37 National Physical Laboratories Teddington Middlesex 1974."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6048-6"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01588953"},{"key":"e_1_2_1_14_2","unstructured":"J. G.Klincewicz Algorithms for Network Flow Problems with Convex Separable Costs. Ph. D. Thesis Yale University 1979."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800230403"},{"key":"e_1_2_1_16_2","volume-title":"Introduction to Linear and Nonlinear Programming","author":"Luenberger D. G.","year":"1973"},{"key":"e_1_2_1_17_2","volume-title":"Computers and Mathematical Programming","author":"Meyer R. 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