{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T10:57:24Z","timestamp":1762340244120},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,2,19]],"date-time":"2009-02-19T00:00:00Z","timestamp":1235001600000},"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":[[2011,1]]},"DOI":"10.1007\/s10589-009-9237-6","type":"journal-article","created":{"date-parts":[[2009,2,18]],"date-time":"2009-02-18T16:26:31Z","timestamp":1234974391000},"page":"23-44","source":"Crossref","is-referenced-by-count":17,"title":["Superrelaxation and the rate of convergence in minimizing quadratic functions subject to bound constraints"],"prefix":"10.1007","volume":"48","author":[{"given":"Zden\u011bk","family":"Dost\u00e1l","sequence":"first","affiliation":[]},{"given":"Marta","family":"Domor\u00e1dov\u00e1","sequence":"additional","affiliation":[]},{"given":"Marie","family":"Sadowsk\u00e1","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,2,19]]},"reference":[{"key":"9237_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511624100","volume-title":"Iterative Solution Methods","author":"O. Axelsson","year":"1994","unstructured":"Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)"},{"key":"9237_CR2","volume-title":"Nonlinear Programming","author":"M.S. Bazaraa","year":"1979","unstructured":"Bazaraa, M.S., Shetty, C.M.: Nonlinear Programming. Wiley, New York (1979)"},{"key":"9237_CR3","volume-title":"Nonlinear Optimization","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas, D.P.: Nonlinear Optimization. Athena Scientific, Belmont (1999)"},{"key":"9237_CR4","first-page":"67","volume":"7","author":"R.H. Bielschowski","year":"1997","unstructured":"Bielschowski, R.H., Friedlander, A., Gomes, F.A.M., Mart\u00ednez, J.M., Raydan, M.: An adaptive algorithm for bound constrained quadratic minimization. Investig. Oper. 7, 67\u2013102 (1997)","journal-title":"Investig. Oper."},{"key":"9237_CR5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s00607-008-0257-3","volume":"82","author":"J. Bouchala","year":"2008","unstructured":"Bouchala, J., Dost\u00e1l, Z., Sadowsk\u00e1, M.: Theoretically supported scalable BETI method for variational inequalities. Computing 82, 53\u201375 (2008)","journal-title":"Computing"},{"key":"9237_CR6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF02592073","volume":"39","author":"P.H. Calamai","year":"1987","unstructured":"Calamai, P.H., Mor\u00e9, J.J.: Projected gradient methods for linearly constrained problems. Math. Program. 39, 93\u2013116 (1987)","journal-title":"Math. Program."},{"issue":"5","key":"9237_CR7","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1023\/A:1013752209845","volume":"46","author":"M.A. Diniz-Ehrhardt","year":"2001","unstructured":"Diniz-Ehrhardt, M.A., Dost\u00e1l, Z., Gomes-Ruggiero, M.A., Mart\u00ednez, J.M., Santos, S.A.: Nonmonotone strategy for minimization of quadratics with simple constraints. Appl. Math. 46(5), 321\u2013338 (2001)","journal-title":"Appl. Math."},{"key":"9237_CR8","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/10556780108805810","volume":"15","author":"M.A. Diniz-Ehrhardt","year":"2001","unstructured":"Diniz-Ehrhardt, M.A., Gomes-Ruggiero, M.A., Santos, S.A.: Numerical analysis of the leaving-face criterion in bound-constrained quadratic minimization. Optim. Methods Softw. 15, 45\u201366 (2001)","journal-title":"Optim. Methods Softw."},{"issue":"10","key":"9237_CR9","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1002\/nla.555","volume":"14","author":"M. Domor\u00e1dov\u00e1","year":"2007","unstructured":"Domor\u00e1dov\u00e1, M., Dost\u00e1l, Z.: Projector preconditioning for partially bound constrained quadratic optimization. Numer. Linear Algebra Appl. 14(10), 791\u2013806 (2007)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"3","key":"9237_CR10","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1137\/S1052623494266250","volume":"7","author":"Z. Dost\u00e1l","year":"1997","unstructured":"Dost\u00e1l, Z.: Box constrained quadratic programming with proportioning and projections. SIAM J. Optim. 7(3), 871\u2013887 (1997)","journal-title":"SIAM J. Optim."},{"key":"9237_CR11","first-page":"25","volume":"38","author":"Z. Dost\u00e1l","year":"1999","unstructured":"Dost\u00e1l, Z.: Inexact solution of auxiliary problems in Polyak type algorithms. Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 38, 25\u201330 (1999)","journal-title":"Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math."},{"issue":"2\u20134","key":"9237_CR12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/B:NUMA.0000005347.98806.b2","volume":"34","author":"Z. Dost\u00e1l","year":"2003","unstructured":"Dost\u00e1l, Z.: A proportioning based algorithm for bound constrained quadratic programming with the rate of convergence. Numer. Algorithms 34(2\u20134), 293\u2013302 (2003)","journal-title":"Numer. Algorithms"},{"key":"9237_CR13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/s00607-006-0184-0","volume":"78","author":"Z. Dost\u00e1l","year":"2006","unstructured":"Dost\u00e1l, Z.: An optimal algorithm for bound and equality constrained quadratic programming problems with bounded spectrum. Computing 78, 311\u2013328 (2006)","journal-title":"Computing"},{"issue":"2","key":"9237_CR14","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1137\/050639454","volume":"45","author":"Z. Dost\u00e1l","year":"2007","unstructured":"Dost\u00e1l, Z.: Inexact semi-monotonic Augmented Lagrangians with optimal feasibility convergence for quadratic programming with simple bounds and equality constraints. SIAM J. Numer. Anal. 45(2), 500\u2013513 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"9237_CR15","first-page":"25","volume":"31","author":"Z. Dost\u00e1l","year":"2008","unstructured":"Dost\u00e1l, Z.: On the decrease of a quadratic function along the projected-gradient path. ETNA 31, 25\u201359 (2008)","journal-title":"ETNA"},{"key":"9237_CR16","series-title":"SOIA","volume-title":"Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities","author":"Z. Dost\u00e1l","year":"2009","unstructured":"Dost\u00e1l, Z.: Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities. SOIA, vol.\u00a023. Springer, New York (2009)"},{"issue":"3\u20136","key":"9237_CR17","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0378-4754(02)00088-5","volume":"61","author":"Z. Dost\u00e1l","year":"2003","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D.: Scalability and FETI based algorithm for large discretized variational inequalities. Math. Comput. Simul. 61(3\u20136), 347\u2013357 (2003)","journal-title":"Math. Comput. Simul."},{"issue":"5\u20136","key":"9237_CR18","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/nla.355","volume":"11","author":"Z. Dost\u00e1l","year":"2004","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D.: Scalable FETI with optimal dual penalty for variational inequalities. Numer. Linear Algebra Appl. 11(5\u20136), 455\u2013472 (2004)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"2","key":"9237_CR19","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1137\/050639454","volume":"45","author":"Z. Dost\u00e1l","year":"2007","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D.: Theoretically supported scalable FETI for numerical solution of variational inequalities. SIAM J. Numer. Anal. 45(2), 500\u2013513 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9237_CR20","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10589-005-4557-7","volume":"30","author":"Z. Dost\u00e1l","year":"2005","unstructured":"Dost\u00e1l, Z., Sch\u00f6berl, J.: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Comput. Optim. Appl. 30(1), 23\u201344 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"9237_CR21","volume-title":"High Performance Software for Non-linear Optimization","author":"Z. Dost\u00e1l","year":"1998","unstructured":"Dost\u00e1l, Z., Friedlander, A., Santos, S.A.: Adaptive precision control in quadratic programming with simple bounds and\/or equalities. In: De Leone, R., Murli, A., Pardalos, P.M., Toraldo, G. (eds.) High Performance Software for Non-linear Optimization. Kluwer Academic, Dordrecht (1998). Appl. Optim. 24, 161\u2013173"},{"issue":"1\u20132","key":"9237_CR22","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/S0377-0427(99)00368-4","volume":"126","author":"Z. Dost\u00e1l","year":"2000","unstructured":"Dost\u00e1l, Z., Gomes, F.A.M., Santos, S.A.: Duality based domain decomposition with natural coarse space for variational inequalities. J. Comput. Appl. Math. 126(1\u20132), 397\u2013415 (2000)","journal-title":"J. Comput. Appl. Math."},{"issue":"13\u201314","key":"9237_CR23","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1016\/S0045-7825(00)00180-8","volume":"190","author":"Z. Dost\u00e1l","year":"2000","unstructured":"Dost\u00e1l, Z., Gomes, F.A.M., Santos, S.A.: Solution of Contact problems by FETI domain decomposition with natural coarse space projection. Comput. Methods Appl. Mech. Eng. 190(13\u201314), 1611\u20131627 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"4","key":"9237_CR24","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1137\/S1052623499362573","volume":"13","author":"Z. Dost\u00e1l","year":"2003","unstructured":"Dost\u00e1l, Z., Friedlander, A., Santos, S.A.: Augmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints. SIAM J. Optim. 13(4), 1120\u20131140 (2003)","journal-title":"SIAM J. Optim."},{"issue":"3\u20134","key":"9237_CR25","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.apnum.2004.09.009","volume":"54","author":"Z. Dost\u00e1l","year":"2005","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D., Stefanica, D.: A scalable FETI\u2013DP algorithm for coercive variational inequalities. IMACS J. Appl. Numer. Math. 54(3\u20134), 378\u2013390 (2005)","journal-title":"IMACS J. Appl. Numer. Math."},{"key":"9237_CR26","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D., Stefanica, D.: A Scalable FETI\u2013DP algorithm with non-penetration mortar conditions on contact interface (2007, submitted)"},{"issue":"8","key":"9237_CR27","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1016\/j.cma.2006.03.025","volume":"196","author":"Z. Dost\u00e1l","year":"2007","unstructured":"Dost\u00e1l, Z., Hor\u00e1k, D., Stefanica, D.: A scalable FETI\u2013DP algorithm for semi-coercive variational inequalities. Comput. Methods Appl. Mech. Eng. 196(8), 1369\u20131379 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9237_CR28","series-title":"Lecture Notes in Computational Science and Engineering (LNCSE)","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/978-3-540-75199-1_30","volume-title":"Domain Methods in Science and Engineering XVII","author":"Z. Dost\u00e1l","year":"2008","unstructured":"Dost\u00e1l, Z., Vondr\u00e1k, V., Hor\u00e1k, D., Farhat, C., Avery, P.: Scalable FETI algorithms for frictionless contact problems. In: Langer, U., (eds.) Domain Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering (LNCSE), vol. 60, pp. 263\u2013270. Springer, Berlin (2008)"},{"key":"9237_CR29","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1137\/0804010","volume":"4","author":"A. Friedlander","year":"1994","unstructured":"Friedlander, A., Mart\u00ednez, M.: On the maximization of a concave quadratic function with box constraints. SIAM J. Optim. 4, 177\u2013192 (1994)","journal-title":"SIAM J. Optim."},{"key":"9237_CR30","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF01183013","volume":"30","author":"A. Friedlander","year":"1994","unstructured":"Friedlander, A., Mart\u00ednez, J.M., Santos, S.A.: A new trust region algorithm for bound constrained minimization. Appl. Math. Optim. 30, 235\u2013266 (1994)","journal-title":"Appl. Math. Optim."},{"key":"9237_CR31","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1080\/10556789508805602","volume":"5","author":"A. Friedlander","year":"1995","unstructured":"Friedlander, A., Mart\u00ednez, J.M., Raydan, M.: A new method for large scale box constrained quadratic minimization problems. Optim. Methods Softw. 5, 57\u201374 (1995)","journal-title":"Optim. Methods Softw."},{"key":"9237_CR32","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970937","volume-title":"Iterative Methods for Solving Linear Systems","author":"A. Greenbaum","year":"1997","unstructured":"Greenbaum, A.: Iterative Methods for Solving Linear Systems. SIAM, Philadelphia (1997)"},{"issue":"2","key":"9237_CR33","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1137\/050635225","volume":"17","author":"W.W. Hager","year":"2006","unstructured":"Hager, W.W., Zhang, H.: A new active set algorithm for box constrained optimization. SIAM J. Optim. 17(2), 526\u2013557 (2006)","journal-title":"SIAM J. Optim."},{"key":"9237_CR34","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1137\/S1052623401383558","volume":"13","author":"M. Hinterm\u00fcller","year":"2003","unstructured":"Hinterm\u00fcller, M., Ito, K., Kunisch, K.: The primal\u2013dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13, 865\u2013888 (2003)","journal-title":"SIAM J. Optim."},{"key":"9237_CR35","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1137\/060671061","volume":"30","author":"S. H\u00fceber","year":"2008","unstructured":"H\u00fceber, S., Stadler, G., Wohlmuth, B.I.: A primal-dual active set algorithm for three-dimensional contact problems with coulomb friction. SIAM J. Sci. Comput. 30, 572\u2013596 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"9237_CR36","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF02096261","volume":"46","author":"Z.-Q. Luo","year":"1993","unstructured":"Luo, Z.-Q., Tseng, P.: Error bounds and convergence analysis of feasible descent methods: a general approach. Ann. Oper. Res. 46, 157\u2013178 (1993)","journal-title":"Ann. Oper. Res."},{"key":"9237_CR37","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1137\/0801008","volume":"1","author":"J.J. Mor\u00e9","year":"1991","unstructured":"Mor\u00e9, J.J., Toraldo, G.: On the solution of large quadratic programming problems with bound constraints. SIAM J. Optim. 1, 93\u2013113 (1991)","journal-title":"SIAM J. Optim."},{"key":"9237_CR38","unstructured":"Lesoinne, M., Dost\u00e1l, Z.: Accelerating contact area detection in FETI-DPC methods. In: Lecture at 16th Int. Conference on Domain Decomposition Methods, New York City (2005)"},{"key":"9237_CR39","volume-title":"Numerical Optimization","author":"J. Nocedal","year":"2000","unstructured":"Nocedal, J., Wright, S.F.: Numerical Optimization. Springer, New York (2000)"},{"key":"9237_CR40","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/0041-5553(69)90035-4","volume":"9","author":"B.T. Polyak","year":"1969","unstructured":"Polyak, B.T.: The conjugate gradient method in extremal problems. USSR Comput. Math. Math. Phys. 9, 94\u2013112 (1969)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"9237_CR41","volume-title":"Scalable Total Beti for 2D and 3D Contact Problems","author":"M. Sadowsk\u00e1","year":"2008","unstructured":"Sadowsk\u00e1, M.: Scalable Total Beti for 2D and 3D Contact Problems. FEI V\u0160B-TU Ostrava, Ostrava (2008)"},{"issue":"4","key":"9237_CR42","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF02684379","volume":"60","author":"J. Sch\u00f6berl","year":"1998","unstructured":"Sch\u00f6berl, J.: Solving the Signorini problem on the basis of domain decomposition techniques. Computing 60(4), 323\u2013344 (1998)","journal-title":"Computing"},{"key":"9237_CR43","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1016\/S0898-1221(01)00234-6","volume":"42","author":"J. Sch\u00f6berl","year":"2001","unstructured":"Sch\u00f6berl, J.: Efficient contact solvers based on domain decomposition techniques. Int. J. Comput. Math. Appl. 42, 1217\u20131228 (2001)","journal-title":"Int. J. Comput. Math. Appl."},{"key":"9237_CR44","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/BF01389450","volume":"48","author":"A. Sluis van der","year":"1986","unstructured":"van der Sluis, A., van der Vorst, H.A.: The rate of convergence of the conjugate gradients. Numer. Math. 48, 543\u2013560 (1986)","journal-title":"Numer. Math."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9237-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9237-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9237-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:36Z","timestamp":1559302596000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9237-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,19]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["9237"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9237-6","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,19]]}}}