{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T23:22:34Z","timestamp":1751930554291},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T00:00:00Z","timestamp":1172102400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2007,4]]},"DOI":"10.1007\/s10589-006-9007-7","type":"journal-article","created":{"date-parts":[[2007,2,21]],"date-time":"2007-02-21T17:47:09Z","timestamp":1172080029000},"page":"165-193","source":"Crossref","is-referenced-by-count":16,"title":["Stopping criteria for inner iterations in inexact potential reduction methods: a computational study"],"prefix":"10.1007","volume":"36","author":[{"given":"S.","family":"Cafieri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"D\u2019Apuzzo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"De Simone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"di Serafino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,2,22]]},"reference":[{"key":"9007_CR1","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/978-1-4613-3449-1_6","volume-title":"Interior Point Methods in Mathematical Programming","author":"E.D. Andersen","year":"1996","unstructured":"Andersen, E.D., Gondzio, J., Meszaros, C., Xu, X.: Implementation of interior point methods for large scale linear programming. In: Terlaky, T. (ed.) Interior Point Methods in Mathematical Programming, pp. 189\u2013252. Kluwer Academic, Dordrecht (1996)"},{"key":"9007_CR2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1023\/A:1022663100715","volume":"96","author":"S. Bellavia","year":"1998","unstructured":"Bellavia, S.: Inexact interior point method. J. Optim. Theory Appl. 96, 109\u2013121 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"9007_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M. Benzi","year":"2005","unstructured":"Benzi, M., Golub, G., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1\u2013137 (2005)","journal-title":"Acta Numer."},{"issue":"2","key":"9007_CR4","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/B:COAP.0000026882.34332.1b","volume":"28","author":"L. Bergamaschi","year":"2004","unstructured":"Bergamaschi, L., Gondzio, J., Zilli, G.: Preconditioning indefinite systems in interior point methods for optimization. Comput. Optim. Appl. 28(2), 149\u2013171 (2004)","journal-title":"Comput. Optim. Appl."},{"key":"9007_CR5","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/978-1-5041-2940-4_9","volume-title":"The Quality of Numerical Software: Assessment and Enhancement","author":"R. Boisvert","year":"1997","unstructured":"Boisvert, R., Pozo, R., Remington, K., Barrett, R., Dongarra, J.: Matrix Market: a web resource for test matrix collections. In: Boisvert, R. (ed.) The Quality of Numerical Software: Assessment and Enhancement, pp. 125\u2013137. Chapman & Hall, London (1997). See also the Matrix Market home page, http:\/\/math.nist.gov\/MatrixMarket\/"},{"key":"9007_CR6","doi-asserted-by":"crossref","unstructured":"Cafieri, S., D\u2019Apuzzo, M., De Simone, V., di Serafino, D.: On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems. Comput. Optim. Appl. (to appear)","DOI":"10.1007\/s10589-007-9035-y"},{"key":"9007_CR7","doi-asserted-by":"crossref","unstructured":"Cafieri, S., D\u2019Apuzzo, M., De Simone, V., di Serafino, D., Toraldo, G.: On the convergence of inexact potential reduction algorithms for convex quadratic programming. J. Optim. Theory Appl. 133(2), (2007)","DOI":"10.1007\/s10957-007-9264-3"},{"issue":"1","key":"9007_CR8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10957-006-9043-6","volume":"129","author":"S. Cafieri","year":"2006","unstructured":"Cafieri, S., D\u2019Apuzzo, M., Marino, M., Mucherino, A., Toraldo, G.: Interior point solver for large-scale quadratic programming problems with bound constraints. J. Optim. Theory Appl. 129(1), 55\u201375 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"9007_CR9","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1137\/0719025","volume":"19","author":"R.S. Dembo","year":"1982","unstructured":"Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM J. Numer. Anal. 19, 400\u2013408 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"9007_CR10","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Technical Report ANL\/MCS-P861-1200, Argonne National Laboratory (2001)"},{"key":"9007_CR11","unstructured":"Dollar, H.S.: Extending constraint preconditioners for saddle point problems. Technical Report NA-05\/02. Oxford University Computing Laboratory (2005) SIAM J. Matrix Anal. Appl. (submitted)"},{"key":"9007_CR12","unstructured":"Dollar, H.S., Gould, N.I.M., Wathen, A.J.: On implicit-factorization constraint preconditioners. Technical Report, RAL-TR-2004-036. Rutherford Appleton Laboratory (2004)"},{"key":"9007_CR13","unstructured":"Dollar, H.S., Gould, N.I.M., Schilders, W.H.A., Wathen, A.J.: On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems. Technical Report, RAL-TR-2005-011. Rutherford Appleton Laboratory (2005)"},{"issue":"3","key":"9007_CR14","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1145\/356044.356047","volume":"9","author":"I.S. Duff","year":"1983","unstructured":"Duff, I.S., Reid, J.K.: The multifrontal solution of indefinite sparse symmetric linear equations. ACM Trans. Math. Software 9(3), 302\u2013325 (1983)","journal-title":"ACM Trans. Math. Software"},{"issue":"8","key":"9007_CR15","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1002\/nla.308","volume":"10","author":"C. Durazzi","year":"2003","unstructured":"Durazzi, C., Ruggiero, V.: Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems. Numer. Linear Algebra Appl. 10(8), 673\u2013688 (2003)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9007_CR16","unstructured":"Forsgren, A., Gill, P.E., Griffin, J.D.: Iterative solution of augmented systems arising in interior methods. Technical Report NA-05-03, UCSD Department of Mathematics (2005)"},{"issue":"4","key":"9007_CR17","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144502414942","volume":"44","author":"A. Forsgren","year":"2002","unstructured":"Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Rev. 44(4), 525\u2013597 (2002)","journal-title":"SIAM Rev."},{"key":"9007_CR18","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/978-1-4757-3216-0_18","volume-title":"High Performance Optimization","author":"R.M. Freund","year":"2000","unstructured":"Freund, R.M., Mizuno, S.: Interior point methods: current status and future directions. In: Frenk, H. et al. (eds.) High Performance Optimization, pp. 441\u2013466. Kluwer Academic, Dordrecht (2000)"},{"key":"9007_CR19","volume-title":"Large-Scale Numerical Optimization","author":"C.G. Han","year":"1990","unstructured":"Han, C.G., Pardalos, P.M., Ye, Y.: Computational aspects of an interior point algorithm for quadratic programming problems with box constraints. In: Coleman, T., Li, Y. (eds.) Large-Scale Numerical Optimization, SIAM, Philadelphia (1990)"},{"key":"9007_CR20","unstructured":"Haws, J., Mayer, C.: Preconditioning KKT systems. Technical Report M&CT-Tech-01-021, the Boeing Co. (2001)"},{"key":"9007_CR21","first-page":"245","volume":"14","author":"S. Ito","year":"1995","unstructured":"Ito, S.: Inexact implementation of interior point algorithms for optimal control problems. Lect. Notes Numer. Appl. Anal. 14, 245\u2013248 (1995)","journal-title":"Lect. Notes Numer. Appl. Anal."},{"issue":"4","key":"9007_CR22","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1137\/S0895479899351805","volume":"21","author":"C. Keller","year":"2000","unstructured":"Keller, C., Gould, N., Wathen, A.: Constraint preconditioning for indefinite linear systems. SIAM J. Matrix Anal. Appl. 21(4), 1300\u20131317 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"9007_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/(SICI)1099-1506(199601\/02)3:1<1::AID-NLA67>3.0.CO;2-E","volume":"3","author":"R.D. Lazarov","year":"1996","unstructured":"Lazarov, R.D., Vassilevski, P.S.: Preconditioning saddle-point problems arising from mixed finite element discretizations of elliptic equations. Numer. Linear Algebra Appl. 3(1), 1\u201320 (1996)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9007_CR24","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1002\/(SICI)1099-1506(199805\/06)5:3<219::AID-NLA134>3.0.CO;2-7","volume":"5","author":"L. Luksan","year":"1998","unstructured":"Luksan, L., Vlcek, J.: Indefinitely preconditioned inexact Newton method for large sparse equality constrained nonlinear programming problems. Numer. Linear Algebra Appl. 5, 219\u2013247 (1998)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9007_CR25","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1137\/0805003","volume":"5","author":"S. Mizuno","year":"1995","unstructured":"Mizuno, S., Kojima, M., Todd, M.J.: Infeasible-interior-point primal\u2013dual potential-reduction algorithms for linear programming. SIAM J. Optim. 5, 52\u201367 (1995)","journal-title":"SIAM J. Optim."},{"key":"9007_CR26","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/978-1-4613-3449-1_12","volume-title":"Interior Point Methods of Mathematical Programming","author":"P.M. Pardalos","year":"1996","unstructured":"Pardalos, P.M., Resende, M.G.C.: Interior point methods for global optimization problems. In: Terlaky, T. (ed.) Interior Point Methods of Mathematical Programming, pp. 467\u2013500. Kluwer Academic, Dordrecht (1996)"},{"key":"9007_CR27","volume-title":"Handbook of Applied Optimization","year":"2002","unstructured":"Pardalos, P.M., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, Oxford (2002)"},{"issue":"7\u20138","key":"9007_CR28","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<585::AID-NLA214>3.0.CO;2-F","volume":"7","author":"I. Perugia","year":"2000","unstructured":"Perugia, I., Simoncini, V.: Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations. Numer. Linear Algebra Appl. 7(7\u20138), 585\u2013616 (2000)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"2","key":"9007_CR29","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/S0895479800375540","volume":"24","author":"M. Rozloznik","year":"2002","unstructured":"Rozloznik, M., Simoncini, V.: Krylov subspace methods for saddle point problems with indefinite preconditioning. SIAM J. Matrix Anal. Appl. 24(2), 368\u2013391 (2002)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9007_CR30","unstructured":"Baryamureeba, V., Steihaug, T.: On the convergence of an inexact primal\u2013dual interior point method for linear programming. Reports in Informatics No. 188, Department of Informatics, University of Bergen, Norway (2000)"},{"key":"9007_CR31","series-title":"Lecture Notes in Control and Information Systems","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BFb0042787","volume-title":"System Modeling and Optimization: Proceedings of the 13th IFIP Conference","author":"K. Tanabe","year":"1988","unstructured":"Tanabe, K.: Centered Newton method for mathematical programming. In: Iri, M., Yajima, K. (eds.) System Modeling and Optimization: Proceedings of the 13th IFIP Conference. Lecture Notes in Control and Information Systems, vol. 113, pp. 197\u2013206. Springer, New York (1988)"},{"key":"9007_CR32","first-page":"3","volume":"76","author":"M.J. Todd","year":"1996","unstructured":"Todd, M.J.: Potential-reduction methods in mathematical programming. Math. Program. 76, 3\u201345 (1996)","journal-title":"Math. Program."},{"key":"9007_CR33","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1287\/moor.15.3.508","volume":"15","author":"M.J. Todd","year":"1990","unstructured":"Todd, M.J., Ye, Y.: A centered projective algorithm for linear programming. Math. Oper. Res. 15, 508\u2013529 (1990)","journal-title":"Math. Oper. Res."},{"key":"9007_CR34","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971453","volume-title":"Primal\u2013Dual Interior-Point Methods","author":"S.J. Wright","year":"1997","unstructured":"Wright, S.J.: Primal\u2013Dual Interior-Point Methods. SIAM, Philadelphia (1997)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-9007-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-006-9007-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-006-9007-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:30Z","timestamp":1559302590000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-006-9007-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,22]]},"references-count":34,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2007,4]]}},"alternative-id":["9007"],"URL":"https:\/\/doi.org\/10.1007\/s10589-006-9007-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,22]]}}}