{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T19:39:29Z","timestamp":1760384369967},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2004,11,1]],"date-time":"2004-11-01T00:00:00Z","timestamp":1099267200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2004,11]]},"DOI":"10.1007\/s10898-004-8276-x","type":"journal-article","created":{"date-parts":[[2005,2,18]],"date-time":"2005-02-18T13:35:50Z","timestamp":1108733750000},"page":"285-300","source":"Crossref","is-referenced-by-count":11,"title":["Convergence Properties of Dikin\u2019s Affine Scaling Algorithm for Nonconvex Quadratic Minimization"],"prefix":"10.1007","volume":"30","author":[{"given":"Paul","family":"Tseng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"8276_CR1","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1007\/BF02592024","volume":"36","author":"E. R. Barnes","year":"1986","unstructured":"Barnes, E. R. (1986), A variation on Karmarkar\u2019s algorithm for solving linear programming problems, Mathematical Programming 36, 174-182.","journal-title":"Mathematical Programming"},{"key":"8276_CR2","first-page":"195","volume":"29","author":"J. F. Bonnans","year":"1995","unstructured":"Bonnans, J. F. and Bouhtou, M. (1995), The trust region affine interior point algorithm for convex and nonconvex quadratic programming, RAIRO Recherche Op\u00e9rationelle 29, 195-217.","journal-title":"RAIRO Recherche Op\u00e9rationelle"},{"key":"8276_CR3","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1137\/S1052623493250639","volume":"7","author":"J. F. Bonnans","year":"1997","unstructured":"Bonnans, J. F. and Pola, C. (1997), A trust region interior point algorithm for linearly constrained optimization, SIAM Journal on Optimization 7, 717-731.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR4","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1137\/S1052623496314070","volume":"11","author":"I. Castillo","year":"2000","unstructured":"Castillo, I. and Barnes, E. R. (2000), Chaotic behavior of the affine scaling algorithm for linear programming, SIAM Journal on Optimization 11, 781-795.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR5","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"A. R. Conn","year":"2000","unstructured":"Conn, A. R., Gould, N. I. M. and Toint, P. L. (2000), Trust-Region Methods, SIAM Publication, Philadelphia, PA."},{"key":"8276_CR6","first-page":"674","volume":"8","author":"I. I. Dikin","year":"1967","unstructured":"Dikin, I. I. (1967), Iterative solution of problems of linear and quadratic programming, Soviet Mathematics Doklady 8, 674-675.","journal-title":"Soviet Mathematics Doklady"},{"key":"8276_CR7","first-page":"54","volume":"12","author":"I. I. Dikin","year":"1974","unstructured":"Dikin, I. I. (1974), On the speed of an iterative process, Upravlyaemye Sistemi 12, 54-60.","journal-title":"Upravlyaemye Sistemi"},{"key":"8276_CR8","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/BF01580777","volume":"41","author":"I. I. Dikin","year":"1988","unstructured":"Dikin, I. I. (1988), Letter to the Editor, Mathematical Programming 41, 393-394.","journal-title":"Mathematical Programming"},{"key":"8276_CR9","volume-title":"The convergence of dualvariables","author":"I. I. Dikin","year":"1991","unstructured":"Dikin, I. I. (1991), The convergence of dualvariables, Tech. Report, Siberian Energy Institute, Irkutsk, Russia."},{"key":"8276_CR10","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1023\/A:1022683121151","volume":"95","author":"I. I. Dikin","year":"1997","unstructured":"Dikin, I. I. and Roos, C. (1997), Convergence of the dualvariables for the primal affine scaling method with unit steps in the homogeneous case, Journal of Optimization Theory and Applications 95, 305-321.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"8276_CR11","series-title":"Tech. Report","volume-title":"Convergence of the large step primal affine-scaling algorithm for primalnondegenerate linear programs","author":"C. C. Gonzaga","year":"1990","unstructured":"Gonzaga, C. C. (1990), Convergence of the large step primal affine-scaling algorithm for primalnondegenerate linear programs, Tech. Report ES-230\/90, Department of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro, Rio de Janeiro, Brazil."},{"key":"8276_CR12","series-title":"Tech. Report","volume-title":"A primal affine-scaling algorithm for linearly constrained convex programs","author":"C. C. Gonzaga","year":"1990","unstructured":"Gonzaga, C. C. and Carlos, L. A. (1990), A primal affine-scaling algorithm for linearly constrained convex programs, Tech. Report ES-238\/90, Department of Systems Engineering and Computer Science, COPPE Federal University of Rio de Janeiro, Rio de Janeiro, Brazil."},{"key":"8276_CR13","doi-asserted-by":"crossref","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"A. J. Hoffman","year":"1952","unstructured":"Hoffman, A. J. (1952), On approximate solutions of systems of linear inequalities, Journal of Research of the National Bureau of Standards 49, 263-265.","journal-title":"Journal of Research of the National Bureau of Standards"},{"key":"8276_CR14","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N. Karmarkar","year":"1984","unstructured":"Karmarkar, N. (1984), A new polynomial-time algorithm for linear programming, Combinatorica 4, 373-395.","journal-title":"Combinatorica"},{"key":"8276_CR15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1137\/0802004","volume":"2","author":"Z.-Q. Luo","year":"1992","unstructured":"Luo, Z.-Q. and Tseng, P. (1992), Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem, SIAM Journal on Optimization 2, 43-54.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR16","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1137\/S1052623493258404","volume":"7","author":"W. F. Mascarenhas","year":"1997","unstructured":"Mascarenhas, W. F. (1997), The affine scaling algorithm fails for stepsize 0 999, SIAM Journal on Optimization 7, 34-46.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR17","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0167-6377(87)90040-X","volume":"6","author":"C. L. Monma","year":"1987","unstructured":"Monma, C. L. and Morton, A. J. (1987), Computationalexperiments with a dual affine variant of Karmarkar \u2018s method for linear programming, Operations Research Letters 6, 261-267.","journal-title":"Operations Research Letters"},{"key":"8276_CR18","first-page":"77","volume":"75","author":"R. D. C. Monteiro","year":"1996","unstructured":"Monteiro, R. D. C. and Tsuchiya, T. (1996), Superlinear convergence of the affine scaling algorithm, Mathematical Programming 75, 77-110.","journal-title":"Mathematical Programming"},{"key":"8276_CR19","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1137\/S1052623495283851","volume":"8","author":"R. D. C. Monteiro","year":"1998","unstructured":"Monteiro, R. D. C. and Tsuchiya, T. (1998), Global convergence of the affine scaling algorithm for convex quadratic programming, SIAM Journal on Optimization 8, 26-58.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR20","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/BF02023109","volume":"46","author":"R. D. C. Monteiro","year":"1993","unstructured":"Monteiro, R. D. C., Tsuchiya, T. and Wang, Y. (1993), A simplified global convergence proof of the affine scaling algorithm, Annals of Operations Research 46\/47, 443-482.","journal-title":"Annals of Operations Research"},{"key":"8276_CR21","first-page":"283","volume":"80","author":"R. D. C. Monteiro","year":"1998","unstructured":"Monteiro, R. D. C. and Wang, Y. (1998), Trust region affine scaling algorithms for linearly constrained convex and concave programs, Mathematical Programming 80, 283-313.","journal-title":"Mathematical Programming"},{"key":"8276_CR22","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF01396045","volume":"55","author":"J. J. Mor\u00e9","year":"1989","unstructured":"Mor\u00e9, J. J. and Toraldo, G. (1989), Algorithm for bound constrained quadratic programming problems, Numerische Mathematik 55, 377-400.","journal-title":"Numerische Mathematik"},{"key":"8276_CR23","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02206822","volume":"62","author":"M. Muramatsu","year":"1996","unstructured":"Muramatsu, M. and Tsuchiya, T. (1996), An affine scaling method with an infeasible starting point: convergence analysis under nondegeneracy assumption, Annals of Operations Research 62, 325-355.","journal-title":"Annals of Operations Research"},{"key":"8276_CR24","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02206821","volume":"62","author":"R. Saigal","year":"1996","unstructured":"Saigal, R. (1996), A simple proof of a primal affine scaling method, Annals of Operations Research 62, 303-324.","journal-title":"Annals of Operations Research"},{"key":"8276_CR25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01580601","volume":"60","author":"J. Sun","year":"1993","unstructured":"Sun, J. (1993), A convergence proof for an affine-scaling algorithm for convex quadratic programming without nondegeneracy assumptions, Mathematical Programming 60, 69-79.","journal-title":"Mathematical Programming"},{"key":"8276_CR26","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02206823","volume":"62","author":"J. Sun","year":"1996","unstructured":"Sun, J. (1996), A convergence analysis for a convex version of Dikin \u2018s algorithm, Annals of Operations Research 62, 357-374.","journal-title":"Annals of Operations Research"},{"key":"8276_CR27","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/s002459900127","volume":"40","author":"T. Terlaky","year":"1999","unstructured":"Terlaky, T. and Tsuchiya, T. (1999), A note on Mascarenhas\u2019 counterexample about global convergence of the affine scaling algorithm, Applied Mathematics and Optimization 40, 287-314.","journal-title":"Applied Mathematics and Optimization"},{"key":"8276_CR28","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/BF01580904","volume":"56","author":"P. Tseng","year":"1992","unstructured":"Tseng, P. and Luo, Z.-Q. (1992), On the convergence of the affine-scaling algorithm, Mathematical Programming 56, 301-319.","journal-title":"Mathematical Programming"},{"key":"8276_CR29","first-page":"217","volume":"93","author":"P. Tseng","year":"2000","unstructured":"Tseng, P. and Ye, Y. (2000), On some interior-point algorithms for nonconvex quadratic optimization, MathematicalProgramming 93, 217-225.","journal-title":"MathematicalProgramming"},{"key":"8276_CR30","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1287\/moor.17.3.527","volume":"17","author":"T. Tsuchiya","year":"1992","unstructured":"Tsuchiya, T. (1992), Global convergence property of the affine scaling methods for primal degenerate linear programming problems, Mathematics of Operations Research 17, 527-557.","journal-title":"Mathematics of Operations Research"},{"key":"8276_CR31","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF01582896","volume":"52","author":"T. Tsuchiya","year":"1991","unstructured":"Tsuchiya, T. (1991), Global convergence of the affine scaling methods for degenerate linear programming problems, Mathematical Programming 52, 377-404.","journal-title":"Mathematical Programming"},{"key":"8276_CR32","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/BF02023112","volume":"46","author":"T. Tsuchiya","year":"1993","unstructured":"Tsuchiya, T. (1993), Global convergence of the affine scaling algorithm for primal degenerate strictly convex quadratic programming problems, Annals of Operations Research 46\/47, 509-539.","journal-title":"Annals of Operations Research"},{"key":"8276_CR33","first-page":"77","volume":"75","author":"T. Tsuchiya","year":"1996","unstructured":"Tsuchiya, T. and Monteiro, R. D. C. (1996), Superlinear convergence of the affine scaling algorithm, Mathematical Programming 75, 77-110.","journal-title":"Mathematical Programming"},{"key":"8276_CR34","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/0805027","volume":"5","author":"T. Tsuchiya","year":"1995","unstructured":"Tsuchiya, T. and Muramatsu, M. (1995), Global convergence of a long-step affine scaling algorithm for degenerate linear programming problems, SIAM Journal on Optimization 5, 525-551.","journal-title":"SIAM Journal on Optimization"},{"key":"8276_CR35","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF01582276","volume":"43","author":"R. J. Vanderbei","year":"1989","unstructured":"Vanderbei, R. J. (1989), Affine-scaling for linear programs with free variables, Mathematical Programming 43, 31-44.","journal-title":"Mathematical Programming"},{"key":"8276_CR36","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0167-6377(93)90040-N","volume":"13","author":"R. J. Vanderbei","year":"1993","unstructured":"Vanderbei, R. J. and Hall, L. A. (1993), Two-thirds is sharp for affine scaling, Operations Research Letters 13, 197-201.","journal-title":"Operations Research Letters"},{"key":"8276_CR37","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1090\/conm\/114\/1097868","volume":"114","author":"R. J. Vanderbei","year":"1990","unstructured":"Vanderbei, R. J. and Lagarias, J. C. (1990), I. I. Dikin \u2018s convergence result for the affine-scaling algorithm. In: Contemporary Mathematics 114, Am. Math. Soc., Providence, pp. 109-119.","journal-title":"Contemporary Mathematics"},{"key":"8276_CR38","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF01840454","volume":"1","author":"R. J. Vanderbei","year":"1986","unstructured":"Vanderbei, R. J., Meketon, M. S., and Freeman, B. A. (1986), A modification of Karmarkar \u2018s linear programming algorithm, Algorithmica 1, 395-407.","journal-title":"Algorithmica"},{"key":"8276_CR39","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/978-1-4613-9617-8_3","volume-title":"Progress in Mathematical Programming: Interior Point and Related Methods","author":"Y. Ye","year":"1989","unstructured":"Ye, Y. (1989), An extension of Karmarkar \u2018s projective algorithm and the trust region method for quadratic programming, In: Progress in Mathematical Programming: Interior Point and Related Methods, Megiddo N., (ed), Springer, Berlin, pp. 49-63."},{"key":"8276_CR40","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF01580903","volume":"56","author":"Y. Ye","year":"1992","unstructured":"Ye, Y. (1992), On affine scaling algorithms for nonconvex quadratic programming, Mathematical Programming 56, 285-300.","journal-title":"Mathematical Programming"},{"key":"8276_CR41","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF01587086","volume":"44","author":"Y. Ye","year":"1989","unstructured":"Ye, Y. and Tse, E. (1989), An extension of Karmarkar \u2018s projective algorithm for convex quadratic programming, Mathematical programming 44, 157-179.","journal-title":"Mathematical programming"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-004-8276-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-004-8276-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-004-8276-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T08:12:03Z","timestamp":1559290323000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-004-8276-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11]]},"references-count":41,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2004,11]]}},"alternative-id":["8276"],"URL":"https:\/\/doi.org\/10.1007\/s10898-004-8276-x","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,11]]}}}