{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T12:57:10Z","timestamp":1773752230472,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2006,11,22]],"date-time":"2006-11-22T00:00:00Z","timestamp":1164153600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2007,11,30]]},"DOI":"10.1007\/s10107-006-0050-z","type":"journal-article","created":{"date-parts":[[2006,11,21]],"date-time":"2006-11-21T15:06:03Z","timestamp":1164121563000},"page":"473-491","source":"Crossref","is-referenced-by-count":53,"title":["Breakpoint searching algorithms for the continuous quadratic knapsack problem"],"prefix":"10.1007","volume":"112","author":[{"given":"Krzysztof C.","family":"Kiwiel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,11,22]]},"reference":[{"key":"50_CR1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1142\/9789814354363_0003","volume-title":"Complexity in Numerical Optimization","author":"P. Berman","year":"1993","unstructured":"Berman P., Kovoor N., Pardalos P.M. (1993) Algorithms for the least-distance problem. In: Pardalos P.M. (ed) Complexity in Numerical Optimization. World Scientific, Singapore, pp. 33\u201356"},{"key":"50_CR2","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1287\/mnsc.27.4.431","volume":"27","author":"G.R. Bitran","year":"1981","unstructured":"Bitran G.R., Hax A.C. (1981) Disaggregation and resource allocation using convex knapsack problems with bounded variables. Manage. Sci. 27, 431\u2013441","journal-title":"Manage. Sci."},{"key":"50_CR3","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/S0167-6377(96)00039-9","volume":"20","author":"K.M. Bretthauer","year":"1997","unstructured":"Bretthauer K.M., Shetty B. (1997) Quadratic resource allocation with generalized upper bounds. Oper. Res. Lett. 20, 51\u201357","journal-title":"Oper. Res. Lett."},{"key":"50_CR4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1287\/ijoc.7.1.109","volume":"7","author":"K.M. Bretthauer","year":"1995","unstructured":"Bretthauer K.M., Shetty B., Syam S. (1995) A branch and bound algorithm for integer quadratic knapsack problems. ORSA J. Comput. 7, 109\u2013116","journal-title":"ORSA J. Comput."},{"key":"50_CR5","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1057\/jors.1996.44","volume":"47","author":"K.M. Bretthauer","year":"1996","unstructured":"Bretthauer K.M., Shetty B., Syam S. (1996) A projection method for the integer quadratic knapsack problem. J. Oper. Res. Soc. 47, 457\u2013462","journal-title":"J. Oper. Res. Soc."},{"key":"50_CR6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0167-6377(84)90010-5","volume":"3","author":"P. Brucker","year":"1984","unstructured":"Brucker P. (1984) An O(n) algorithm for quadratic knapsack problems. Oper. Res. Lett. 3, 163\u2013166","journal-title":"Oper. Res. Lett."},{"key":"50_CR7","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1137\/0724092","volume":"24","author":"P.H. Calamai","year":"1987","unstructured":"Calamai P.H., Mor\u00e9 J.J. (1987) Quasi-Newton updates with bounds. SIAM J. Numer. Anal. 24, 1434\u20131441","journal-title":"SIAM J. Numer. Anal."},{"key":"50_CR8","volume-title":"Introduction to Algorithms","author":"T.H. Cormen","year":"2001","unstructured":"Cormen T.H., Leiserson C.E., Rivest R.L., Stein C. (2001) Introduction to Algorithms, 2nd edn. MIT Press, Cambridge","edition":"2"},{"key":"50_CR9","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1287\/moor.19.1.94","volume":"19","author":"S. Cosares","year":"1994","unstructured":"Cosares S., Hochbaum D.S. (1994) Strongly polynomial algorithms for the quadratic transportation problem with a fixed number of sources. Math. Oper. Res. 19, 94\u2013111","journal-title":"Math. Oper. Res."},{"key":"50_CR10","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1002\/nav.3800330106","volume":"33","author":"R.W. Cottle","year":"1986","unstructured":"Cottle R.W., Duvall S.G., Zikan K. (1986) A Lagrangean relaxation algorithm for the constrained matrix problem. Naval Res. Logist. Quart. 33, 55\u201376","journal-title":"Naval Res. Logist. Quart."},{"key":"50_CR11","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/BF01580223","volume":"6","author":"M. Held","year":"1974","unstructured":"Held M., Wolfe P., Crowder H.P. (1974) Validation of subgradient optimization. Math. Program. 6, 62\u201388","journal-title":"Math. Program."},{"key":"50_CR12","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1007\/BF01588328","volume":"18","author":"K. Helgason","year":"1980","unstructured":"Helgason K., Kennington J., Lall H. (1980) A polynomially bounded algorithm for a singly constrained quadratic program. Math. Program. 18, 338\u2013343","journal-title":"Math. Program."},{"key":"50_CR13","first-page":"269","volume":"69","author":"D.S. Hochbaum","year":"1995","unstructured":"Hochbaum D.S., Hong S.P. (1995) About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Math. Program. 69, 269\u2013309","journal-title":"Math. Program."},{"key":"50_CR14","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.tcs.2005.06.032","volume":"347","author":"K.C. Kiwiel","year":"2005","unstructured":"Kiwiel K.C. (2005) On Floyd and Rivest\u2019s select algorithm. Theor. Comput. Sci. 347, 214\u2013238","journal-title":"Theor. Comput. Sci."},{"key":"50_CR15","doi-asserted-by":"crossref","unstructured":"Kiwiel, K.C.: Bracketing methods for the continuous quadratic knapsack problem. Technical report. Systems Research Institute, Warsaw (2006) (in preparation)","DOI":"10.1007\/s10107-006-0050-z"},{"key":"50_CR16","unstructured":"Kiwiel, K.C.: Variable fixing algorithms for the continuous quadratic knapsack problem. Technical report. Systems Research Institute, Warsaw (2006) (in preparation)"},{"key":"50_CR17","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1287\/opre.23.2.360","volume":"23","author":"H. Luss","year":"1975","unstructured":"Luss H., Gupta S.K. (1975) Allocation of effort resources among competing activities. Oper. Res. 23, 360\u2013366","journal-title":"Oper. Res."},{"key":"50_CR18","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1051\/ro\/1997310100071","volume":"31","author":"N. Maculan","year":"1997","unstructured":"Maculan N., Minoux M., Plateau G. (1997) An O(n) algorithm for projecting a vector on the intersection of a hyperplane and R + n . RAIRO Rech. Op\u00e9r. 31, 7\u201316","journal-title":"RAIRO Rech. Op\u00e9r."},{"key":"50_CR19","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0167-6377(89)90064-3","volume":"8","author":"N. Maculan","year":"1989","unstructured":"Maculan N., de Paula G.G., Jr. (1989) A linear-time median-finding algorithm for projecting a vector on the simplex of R n . Oper. Res. Lett. 8, 219\u2013222","journal-title":"Oper. Res. Lett."},{"key":"50_CR20","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/0167-6377(93)90041-E","volume":"13","author":"N. Megiddo","year":"1993","unstructured":"Megiddo N., Tamir A. (1993) Linear time algorithms for some separable quadratic programming problems. Oper. Res. Lett. 13, 203\u2013211","journal-title":"Oper. Res. Lett."},{"key":"50_CR21","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF00938486","volume":"50","author":"C. Michelot","year":"1986","unstructured":"Michelot C. (1986) A finite algorithm for finding the projection of a point onto the canonical simplex of R n . J. Optim. Theory Appl. 50, 195\u2013200","journal-title":"J. Optim. Theory Appl."},{"key":"50_CR22","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1287\/ijoc.4.2.166","volume":"4","author":"S.S. Nielsen","year":"1992","unstructured":"Nielsen S.S., Zenios S.A. (1992) Massively parallel algorithms for singly constrained convex programs. ORSA J. Comput. 4, 166\u2013181","journal-title":"ORSA J. Comput."},{"key":"50_CR23","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF01585748","volume":"46","author":"P.M. Pardalos","year":"1990","unstructured":"Pardalos P.M., Kovoor N. (1990) An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds. Math. Program. 46, 321\u2013328","journal-title":"Math. Program."},{"key":"50_CR24","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01581193","volume":"55","author":"A.G. Robinson","year":"1992","unstructured":"Robinson A.G., Jiang N., Lerme C.S. (1992) On the continuous quadratic knapsack problem. Math. Program. 55, 99\u2013108","journal-title":"Math. Program."},{"key":"50_CR25","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1057\/jors.1990.121","volume":"41","author":"B. Shetty","year":"1990","unstructured":"Shetty B., Muthukrishnan R. (1990) A parallel projection for the multicommodity network model. J. Oper. Res. Soc. 41, 837\u2013842","journal-title":"J. Oper. Res. Soc."},{"key":"50_CR26","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1002\/net.3230210407","volume":"21","author":"J.A. Ventura","year":"1991","unstructured":"Ventura J.A.(1991) Computational development of a Lagrangian dual approach for quadratic networks. Networks 21, 469\u2013485","journal-title":"Networks"},{"key":"50_CR27","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1287\/mnsc.26.1.34","volume":"26","author":"P.H. Zipkin","year":"1980","unstructured":"Zipkin P.H. (1980) Simple ranking methods for allocation of one resource. Manage. Sci. 26, 34\u201343","journal-title":"Manage. Sci."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0050-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-006-0050-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-006-0050-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T05:50:01Z","timestamp":1559109001000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-006-0050-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,22]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,11,30]]}},"alternative-id":["50"],"URL":"https:\/\/doi.org\/10.1007\/s10107-006-0050-z","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,11,22]]}}}