{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:29:55Z","timestamp":1787333395902,"version":"build-2736575974"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,8]]},"abstract":"<jats:p>By introducing quadratic penalty terms, a strictly convex separable network quadratic program can be reduced to an unconstrained optimization problem whose objective is a continuously differentiable piecewise quadratic function. A recently developed nonsmooth version of Newton's method is applied to the reduced problem. The generalized Newton direction is computed by an iterative procedure which exploits the special network data structures that originated from the network simplex method. New features of the algorithm include the use of min-max bases and a dynamic strategy in computation of the Newton directions. Some preliminary computational results are presented. The results suggest the use of \"warm start\" instead of \"cold start.\"<\/jats:p>","DOI":"10.1137\/s1052623494265359","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"728-745","source":"Crossref","is-referenced-by-count":6,"title":["Applying a Newton Method to Strictly Convex Separable Network Quadratic Programs"],"prefix":"10.1137","volume":"8","author":[{"given":"J.","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Kuo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0325067"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(91)90056-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02288325"},{"key":"R4","unstructured":"H.\u2010G. Chen,\n                      Forward\u2010Backward Splitting Techniques: Theory and Applications\n                      , Ph.D. dissertation, Department of Applied Mathematics, University of Washington, Seattle, 1994."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495290179"},{"key":"R6","unstructured":"V. Chvatal,\n                      Linear Programming\n                      , Freeman & Co. New York, 1983."},{"key":"R7","unstructured":"F. H. Clarke,\n                      Optimization and Nonsmooth Analysis\n                      , John Wiley and Sons, New York, 1983."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.24.7.747"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0710063"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0121178"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120941"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1287\/opre.37.3.353"},{"key":"R13","unstructured":"JackDennis, Matematicheskoe programmirovanie i elektricheskie tsepi, Translated from the English by Ju. F. Ki\u010datov and V. N. Novosel\u2019cev, under the editorship of A. M. Petrovskii\u02d8, with an introduction by D. B. Judin, Izdat. Inostr. Lit., Moscow, 1961, 215\u2013023:B799"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800030109"},{"key":"R15","unstructured":"D. Gabay,\n                      Applications of the method of multipliers to variational inequalities\n                      , in Augmented Lagrangian Methods: Applications to the Solution of Boundary Value Problems, M. Fortin and G. Glowinski, eds., North\u2013Holland, Amsterdam, 1983."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01594924"},{"key":"R17","volume-title":"Constructive real analysis","author":"Goldstein Allen","year":"1967"},{"key":"R18","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , The Johns Hopkins University Press, Baltimore, MD, 1983."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00248762"},{"key":"R20","volume-title":"Network flow, transportation and scheduling","author":"Iri Masao","year":"1969"},{"key":"R21","volume-title":"Algorithms for network programming","author":"Kennington Jeff","year":"1980"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130310"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.20.5.814"},{"key":"R24","unstructured":"H. Markowitz,\n                      Portfolio Selection\n                      , John Wiley and Sons, New York, 1959."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2.2.191"},{"key":"R26","first-page":"253","volume":"1","author":"Mulvey J. M.","year":"1987","journal-title":"Adv. Math. Program. Finan. Plann."},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/0801006"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581275"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581136"},{"key":"R30","unstructured":"R. T. Rockafellar,\n                      Convex Analysis\n                      , Princeton University Press, Princeton, NJ, 1970."},{"key":"R31","volume-title":"Network flows and monotropic optimization","author":"Rockafellar R.","year":"1984"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"J. Sun,\n                      A study on monotropic piecewise quadratic programming\n                      , in Recent Developments in Mathematical Programming, H. I. Kumar, ed., Gordon and Breach Science Publishers, Melbourne, Australia, 1991, pp. 213\u2013236.","DOI":"10.1201\/9780429333439-14"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00056-1"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581083"},{"key":"R35","first-page":"55","volume":"14","author":"Sun J.","year":"1997","journal-title":"Asia\u2010Pacific J. Oper. Res."},{"key":"R36","doi-asserted-by":"crossref","unstructured":"J. Sun, K. Tsai, and L. Qi,\n                      A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems\n                      , in Network Optimization Problems: Algorithms, Applications and Complexity, D. Z. Du and P. M. Pardalos, eds., World Scientific Publishing Co. London, UK, 1993, pp. 281\u2013300.","DOI":"10.1142\/9789812798190_0015"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623494265359","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:56:19Z","timestamp":1787331379000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623494265359"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,8]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,8]]}},"alternative-id":["10.1137\/S1052623494265359"],"URL":"https:\/\/doi.org\/10.1137\/s1052623494265359","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,8]]}}}