{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T16:01:03Z","timestamp":1726848063853},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,2,17]],"date-time":"2012-02-17T00:00:00Z","timestamp":1329436800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2012,3]]},"DOI":"10.1007\/s12532-012-0035-2","type":"journal-article","created":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T04:28:53Z","timestamp":1329366533000},"page":"71-107","source":"Crossref","is-referenced-by-count":55,"title":["A primal\u2013dual regularized interior-point method for convex quadratic programs"],"prefix":"10.1007","volume":"4","author":[{"given":"M. P.","family":"Friedlander","sequence":"first","affiliation":[]},{"given":"D.","family":"Orban","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"issue":"12","key":"35_CR1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1080\/10556789908805754","volume":"11","author":"A. Altman","year":"1999","unstructured":"Altman A., Gondzio J.: Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization. Optim. Methods Softw. 11(12), 275\u2013302 (1999)","journal-title":"Optim. Methods Softw."},{"key":"35_CR2","unstructured":"Altman, A., Gondzio, J. Higher order primal dual method (2009). http:\/\/www.maths.ed.ac.uk\/~gondzio\/software\/hopdm.html"},{"issue":"4","key":"35_CR3","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1137\/06066847X","volume":"18","author":"M.F. Anjos","year":"2007","unstructured":"Anjos M.F., Burer S.: On handling free variables in interior-point methods for conic linear optimization. SIAM J. Optim. 18(4), 1310\u20131325 (2007)","journal-title":"SIAM J. Optim."},{"key":"35_CR4","doi-asserted-by":"crossref","unstructured":"Armand, P., Benoist, J.: Uniform boundedness of the inverse of a jacobian matrix arising in regularized interior-point methods. Math. Program. (2011). doi: 10.1007\/s10107-011-0498-3","DOI":"10.1007\/s10107-011-0498-3"},{"issue":"1","key":"35_CR5","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1002\/nla.610","volume":"16","author":"S. Bellavia","year":"2009","unstructured":"Bellavia S., Gondzio J., Morini B.: Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems. Numer. Linear Algebra Appl. 16(1), 39\u201361 (2009). doi: 10.1002\/nla.610","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"35_CR6","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1137\/0708060","volume":"8","author":"J.R. Bunch","year":"1971","unstructured":"Bunch J.R., Parlett B.N.: Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numer. Anal. 8(4), 639\u2013655 (1971)","journal-title":"SIAM J. Numer. Anal."},{"key":"35_CR7","doi-asserted-by":"crossref","unstructured":"Castro, J., Cuesta, J.: Quadratic regularizations in an interior-point method for primal block-angular problems. Math. Programm., 1\u201331 (2010). doi: 10.1007\/s10107-010-0341-2","DOI":"10.1007\/s10107-010-0341-2"},{"key":"35_CR8","unstructured":"Czyzyk, J., Mehrotra, S., Wagner, M., Wright, S.J.. PCx user guide version 1.1. Technical Report OTC 96\/01, Optimization Technology Center, Evanston (1996). http:\/\/www.mcs.anl.gov\/OTC\/Tools\/PCx"},{"key":"35_CR9","volume-title":"Practical Methods of Optimization","author":"R. Fletcher","year":"1987","unstructured":"Fletcher R.: Practical Methods of Optimization, 2nd edn. Wiley, Chichester (1987)","edition":"2"},{"issue":"4","key":"35_CR10","doi-asserted-by":"crossref","first-page":"1706","DOI":"10.1137\/060669930","volume":"30","author":"M.P. Friedlander","year":"2008","unstructured":"Friedlander M.P., Leyffer S.: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs. SIAM J. Sci. Comput. 30(4), 1706\u20131729 (2008). doi: 10.1137\/060669930","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"35_CR11","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1137\/060675320","volume":"18","author":"M.P. Friedlander","year":"2007","unstructured":"Friedlander M.P., Tseng P.: Exact regularization of convex programs. SIAM J. Optim. 18(4), 1326\u20131350 (2007). doi: 10.1137\/060675320","journal-title":"SIAM J. Optim."},{"issue":"1","key":"35_CR12","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1145\/641876.641880","volume":"29","author":"E.M. Gertz","year":"2003","unstructured":"Gertz E.M., Wright S.J.: Object-oriented software for quadratic programming. ACM Trans. Math. Softw. 29(1), 58\u201381 (2003)","journal-title":"ACM Trans. Math. Softw."},{"key":"35_CR13","doi-asserted-by":"crossref","unstructured":"Gill, P.E., Murray, W., Poncele\u00f3n, D.B., Saunders, M.A.: Solving reduced KKT systems in barrier methods for linear and quadratic programming. Technical Report SOL 91-7, Systems Optimization Laboratory, Stanford University, Stanford (1991)","DOI":"10.21236\/ADA239191"},{"issue":"1","key":"35_CR14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/S0895479893252623","volume":"17","author":"P.E. Gill","year":"1996","unstructured":"Gill P.E., Saunders M.A., Shinnerl J.R.: On the stability of Cholesky factorization for symmetric quasidefinite systems. SIAM J. Matrix Anal. Appl. 17(1), 35\u201346 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"35_CR15","doi-asserted-by":"crossref","unstructured":"Gondzio, J.: Matrix-free interior point method. Comput. Optim. Appl., 1\u201324 (2011). doi: 10.1007\/s10589-010-9361-3","DOI":"10.1007\/s10589-010-9361-3"},{"issue":"4","key":"35_CR16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1145\/962437.962439","volume":"29","author":"N.I.M. Gould","year":"2003","unstructured":"Gould N.I.M., Orban D., Toint P.L.: CUTEr and SifDec, a Constrained and Unconstrained Testing Environment, revisited. ACM Trans. Math. Softw. 29(4), 373\u2013394 (2003)","journal-title":"ACM Trans. Math. Softw."},{"key":"35_CR17","unstructured":"Harwell Subroutine Library: A collection of Fortran codes for large-scale scientific computation. AERE Harwell Laboratory (2000). http:\/\/www.numerical.rl.ac.uk\/hsl"},{"issue":"1","key":"35_CR18","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1006\/jpdc.1997.1404","volume":"48","author":"G. Karypis","year":"1998","unstructured":"Karypis G., Kumar V.: Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48(1), 96\u2013129 (1998)","journal-title":"J. Parallel Distrib. Comput."},{"issue":"1","key":"35_CR19","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1137\/S1064827595287997","volume":"20","author":"G. Karypis","year":"1999","unstructured":"Karypis G., Kumar V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359\u2013392 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"35_CR20","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01582151","volume":"61","author":"M. Kojima","year":"1993","unstructured":"Kojima M., Megiddo N., Mizuno S.: A primal\u2013dual infeasible-interior-point algorithm for linear programming. Math. Program. 61, 263\u2013280 (1993)","journal-title":"Math. Program."},{"issue":"6","key":"35_CR21","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1137\/0317052","volume":"17","author":"O.L. Mangasarian","year":"1979","unstructured":"Mangasarian O.L., Meyer R.R.: Nonlinear perturbation of linear programs. SIAM J. Control Optim. 17(6), 745\u2013752 (1979)","journal-title":"SIAM J. Control Optim."},{"key":"35_CR22","unstructured":"Maros, I., M\u00e9sz\u00e1ros, C.: A repository of convex quadratic programming problems. Optim. Methods Softw. 11, 12, 671\u2013681 (1999) (Special Issue on Interior Point Methods)"},{"issue":"4","key":"35_CR23","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1137\/0802028","volume":"2","author":"S. Mehrotra","year":"1992","unstructured":"Mehrotra S.: On the implementation of a primal\u2013dual interior-point method. SIAM J. Optim. 2(4), 575\u2013601 (1992)","journal-title":"SIAM J. Optim."},{"key":"35_CR24","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/10556789808805689","volume":"9","author":"C. M\u00e9sz\u00e1ros","year":"1998","unstructured":"M\u00e9sz\u00e1ros C.: On free variables in interior point methods. Optim. Methods Softw. 9, 121\u2013139 (1998)","journal-title":"Optim. Methods Softw."},{"key":"35_CR25","unstructured":"Mittelmann, H.: http:\/\/plato.la.asu.edu\/ftp\/ampl_files\/qpdataampl (2006)"},{"key":"35_CR26","unstructured":"Netlib. http:\/\/netlib.org\/lp (2011)"},{"key":"35_CR27","doi-asserted-by":"crossref","unstructured":"Ng, E.G., Peyton, B.W.: Block sparse cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comput. 14(5), 1034\u20131056 (1993). doi: 10.1137\/0914063 . http:\/\/link.aip.org\/link\/?SCE\/14\/1034\/1","DOI":"10.1137\/0914063"},{"key":"35_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2004.08.019","volume":"394","author":"A.R.L. Oliveira","year":"2005","unstructured":"Oliveira A.R.L., Sorensen D.C.: A new class of preconditioners for large-scale linear systems from interior point methods for linear programming. Linear Algebra Appl. 394, 1\u201324 (2005)","journal-title":"Linear Algebra Appl."},{"key":"35_CR29","unstructured":"Orban, D.: NLPy\u2014a large-scale optimization toolkit in Python. Technical Report Cahier du GERAD G-2010-xx, GERAD, Montr\u00e9al (2010). http:\/\/nlpy.sourceforge.net\/ ."},{"key":"35_CR30","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF00934777","volume":"12","author":"R.T. Rockafellar","year":"1973","unstructured":"Rockafellar R.T.: The multiplier method of Hestenes and Powell applied to convex programming. J. Optim. Theory Appl. 12, 555\u2013562 (1973)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"35_CR31","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1287\/moor.1.2.97","volume":"1","author":"R.T. Rockafellar","year":"1976","unstructured":"Rockafellar R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97\u2013116 (1976)","journal-title":"Math. Oper. Res."},{"key":"35_CR32","doi-asserted-by":"crossref","unstructured":"Rusten, T., Winther, R.: A preconditioned iterative method for saddlepoint problems. SIAM J. Matrix Anal. Appl. 13(3), 887\u2013904 (1992). doi: 10.1137\/0613054 . http:\/\/link.aip.org\/link\/?SML\/13\/887\/1","DOI":"10.1137\/0613054"},{"key":"35_CR33","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1007\/BF01739829","volume":"35","author":"M.A. Saunders","year":"1995","unstructured":"Saunders M.A.: Solution of sparse rectangular systems using LSQR and CRAIG. BIT 35, 588\u2013604 (1995)","journal-title":"BIT"},{"key":"35_CR34","first-page":"92","volume-title":"Linear and Nonlinear Conjugate Gradient-Related Methods.","author":"M.A. Saunders","year":"1996","unstructured":"Saunders M.A.: Cholesky-based methods for sparse least squares: The benefits of regularization. In: Adams, L., Nazareth, J.L. (eds) Linear and Nonlinear Conjugate Gradient-Related Methods., pp. 92\u2013100. SIAM, Philadelphia (1996)"},{"key":"35_CR35","unstructured":"Saunders, M.A.: PDCO: Primal\u2013dual interior method for convex objectives (2010). http:\/\/www.stanford.edu\/group\/SOL\/software\/pdco.html"},{"key":"35_CR36","unstructured":"Saunders, M.A., Tomlin, J.A.: Solving regularized linear programs using barrier methods and KKT systems. SOL Report 96-4, Dept. of EESOR, Stanford University (1996)"},{"issue":"3","key":"35_CR37","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/BF00940319","volume":"74","author":"R. Setiono","year":"1992","unstructured":"Setiono R.: Interior proximal point algorithm for linear programs. J. Optim. Theory Appl. 74(3), 425\u2013444 (1992)","journal-title":"J. Optim. Theory Appl."},{"key":"35_CR38","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/0377-2217(94)90031-0","volume":"77","author":"R. Setiono","year":"1994","unstructured":"Setiono R.: Interior dual proximal point algorithm for linear programs. Eur. J. Oper. Res. 77, 96\u2013110 (1994)","journal-title":"Eur. J. Oper. Res."},{"key":"35_CR39","doi-asserted-by":"crossref","unstructured":"Silvester, D., Wathen, A.: Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners. SIAM J. Numer. Anal. 31(5), 1352\u20131367 (1994). doi: 10.1137\/0731070 . http:\/\/link.aip.org\/link\/?SNA\/31\/1352\/1","DOI":"10.1137\/0731070"},{"issue":"1","key":"35_CR40","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1287\/ijoc.6.1.32","volume":"6","author":"R.J. Vanderbei","year":"1994","unstructured":"Vanderbei R.J.: Interior-point methods: algorithms and formulations.. ORSA J. Comput. 6(1), 32\u201334 (1994)","journal-title":"ORSA J. Comput"},{"issue":"1","key":"35_CR41","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1137\/0805005","volume":"5","author":"R.J. Vanderbei","year":"1995","unstructured":"Vanderbei R.J.: Symmetric quasi-definite matrices. SIAM J. Optim. 5(1), 100\u2013113 (1995)","journal-title":"SIAM J. Optim."},{"issue":"(3","key":"35_CR42","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/BF00939565","volume":"65","author":"S.J. Wright","year":"1990","unstructured":"Wright S.J.: Implementing proximal point methods for linear programming. J. Optim. Theory Appl. 65((3), 531\u2013554 (1990)","journal-title":"J. Optim. Theory Appl."},{"key":"35_CR43","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":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-012-0035-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12532-012-0035-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-012-0035-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,23]],"date-time":"2019-06-23T20:08:02Z","timestamp":1561320482000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12532-012-0035-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,17]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["35"],"URL":"https:\/\/doi.org\/10.1007\/s12532-012-0035-2","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,17]]}}}