{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:29:34Z","timestamp":1772296174376,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,10,1]],"date-time":"2011-10-01T00:00:00Z","timestamp":1317427200000},"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":[[2012,7]]},"DOI":"10.1007\/s10589-011-9435-x","type":"journal-article","created":{"date-parts":[[2011,9,30]],"date-time":"2011-09-30T17:45:41Z","timestamp":1317404741000},"page":"757-784","source":"Crossref","is-referenced-by-count":17,"title":["Optimization of mixed variational inequalities arising in flow of viscoplastic materials"],"prefix":"10.1007","volume":"52","author":[{"given":"Juan Carlos","family":"de los Reyes","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,10,1]]},"reference":[{"key":"9435_CR1","volume-title":"Analysis and Control of Nonlinear Infinite Dimensional Systems","author":"V. Barbu","year":"1993","unstructured":"Barbu, V.: Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, New York (1993)"},{"issue":"5933","key":"9435_CR2","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1126\/science.1174217","volume":"324","author":"D. Bonn","year":"2009","unstructured":"Bonn, D., Morton, M.D.: Yield stress fluids slowly yield to analysis. Science 324(5933), 1401\u20131402 (2009)","journal-title":"Science"},{"issue":"3","key":"9435_CR3","first-page":"695","volume":"31","author":"E. Casas","year":"2002","unstructured":"Casas, E., Troltzsch, F.: Error estimates for the finite-element approximation of a semilinear elliptic control problem. Control Cybern. 31(3), 695\u2013712 (2002)","journal-title":"Control Cybern."},{"issue":"1","key":"9435_CR4","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1006\/jdeq.1993.1062","volume":"104","author":"E. Casas","year":"1993","unstructured":"Casas, E., Fern\u00e1ndez, L.A.: Distributed control of systems governed by a general class of quasilinear elliptic equations. J. Differ. Equ. 104(1), 20\u201347 (1993)","journal-title":"J. Differ. Equ."},{"issue":"6","key":"9435_CR5","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1137\/S1064827596299767","volume":"20","author":"T.F. Chan","year":"1999","unstructured":"Chan, T.F., Golub, G.H., Mulet, P.: A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Comput. 20(6), 1964\u20131977 (1999)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"9435_CR6","first-page":"207","volume":"17","author":"S. Clain","year":"1997","unstructured":"Clain, S.: Elliptic operators of divergence type with H\u00f6lder coefficients in fractional Sobolev spaces. Rend. Mat. Appl. 17(2), 207\u2013236 (1997)","journal-title":"Rend. Mat. Appl."},{"key":"9435_CR7","doi-asserted-by":"crossref","DOI":"10.7208\/chicago\/9780226764320.001.0001","volume-title":"Navier-Stokes Equations","author":"P. Constantin","year":"1988","unstructured":"Constantin, P., Foias, C.: Navier-Stokes Equations. University of Chicago Press, Chicago (1988)"},{"key":"9435_CR8","doi-asserted-by":"crossref","first-page":"1629","DOI":"10.1137\/090764438","volume":"49","author":"J.C. Los Reyes De","year":"2011","unstructured":"De Los Reyes, J.C.: Optimal control of a class of variational inequalities of the second kind. SIAM J. Control Optim. 49, 1629\u20131658 (2011)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"9435_CR9","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.cam.2010.02.026","volume":"235","author":"J.C. Reyes De\u00a0los","year":"2010","unstructured":"De\u00a0los\u00a0Reyes, J.C., Gonz\u00e1lez, S.: Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods. J. Comput. Appl. Math. 235(1), 11\u201332 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"9435_CR10","author":"J.C. Reyes De\u00a0los","year":"2011","unstructured":"De\u00a0los\u00a0Reyes, J.C., Gonz\u00e1lez, S.: A combined BDF-semismooth Newton approach for time dependent Bingham flow. Numer. Methods Partial Differ. Equ. (2011). doi: 10.1002\/num.20658","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"1\u20133","key":"9435_CR11","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jnnfm.2006.09.002","volume":"142","author":"E.J. Dean","year":"2007","unstructured":"Dean, E.J., Glowinski, R., Guidoboni, G.: On the numerical simulation of Bingham viscoplastic flow: old and new results. J. Non-Newton. Fluid Mech. 142(1\u20133), 36\u201362 (2007)","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"9435_CR12","volume-title":"Les in\u00e9quations en m\u00e9canique et en physique","author":"G. Duvaut","year":"1972","unstructured":"Duvaut, G., Lions, J.-L.: Les in\u00e9quations en m\u00e9canique et en physique. Dunod, Paris (1972). Travaux et Recherches Math\u00e9matiques, No. 21"},{"issue":"3","key":"9435_CR13","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/PL00004390","volume":"227","author":"M. Fuchs","year":"1998","unstructured":"Fuchs, M., Seregin, G.: Regularity results for the quasi-static Bingham variational inequality in dimensions two and three. Math. Z. 227(3), 525\u2013541 (1998)","journal-title":"Math. Z."},{"key":"9435_CR14","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0103751","volume-title":"Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids","author":"M. Fuchs","year":"2000","unstructured":"Fuchs, M., Seregin, G.: Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids. Lecture Notes in Mathematics, vol. 1749. Springer, Berlin, (2000)"},{"key":"9435_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite Element Methods for Navier-Stokes Equations","author":"V. Girault","year":"1986","unstructured":"Girault, V., Raviart, P.-A.: Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1986)"},{"key":"9435_CR16","series-title":"Springer Series in Computational Physics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12613-4","volume-title":"Numerical Methods for Nonlinear Variational Problems","author":"R. Glowinski","year":"1984","unstructured":"Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer Series in Computational Physics. Springer, Berlin (1984)"},{"key":"9435_CR17","volume-title":"Proceedings of the 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions","author":"F. Gordaninejad","year":"2006","unstructured":"Gordaninejad, F., Graeve, O., Fuchs, A., York, D.: Proceedings of the 10th International Conference on Electrorheological Fluids and Magnetorheological Suspensions. World Scientific, Singapore (2006)"},{"key":"9435_CR18","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1002\/zamm.200900378","volume":"91","author":"R. Herzog","year":"2011","unstructured":"Herzog, R., Meyer, C.: Optimal control of static plasticity with linear kinematic hardening. Z. Angew. Math. Mech. 91, 777\u2013794 (2011)","journal-title":"Z. Angew. Math. Mech."},{"issue":"6","key":"9435_CR19","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1137\/0732081","volume":"32","author":"W. Han","year":"1995","unstructured":"Han, W., Reddy, B.D.: On the finite element method for mixed variational inequalities arising in elastoplasticity. SIAM J. Numer. Anal. 32(6), 1778\u20131807 (1995)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"9435_CR20","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1137\/S1052623401383558","volume":"13","author":"M. Hinterm\u00fcller","year":"2002","unstructured":"Hinterm\u00fcller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13(3), 865\u2013888 (2002)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"9435_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/040613263","volume":"28","author":"M. Hinterm\u00fcller","year":"2006","unstructured":"Hinterm\u00fcller, M., Stadler, G.: An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration. SIAM J. Sci. Comput. 28(1), 1\u201323 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9435_CR22","series-title":"Handbook of Numerical Analysis","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/B978-0-444-53047-9.00007-1","volume-title":"Numerical Methods for Non-Newtonian Fluids","author":"R.H.W. Hoppe","year":"2011","unstructured":"Hoppe, R.H.W., Litvinov, W.G.: Modeling, simulation and optimization of electrorheological fluids. In: Glowinski, R., Xu, J. (eds.) Numerical Methods for Non-Newtonian Fluids. Handbook of Numerical Analysis, vol. 16, pp. 719\u2013793. Elsevier, Amsterdam (2011)"},{"key":"9435_CR23","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1038\/nature04801","volume":"441","author":"P. Jop","year":"2006","unstructured":"Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441, 727\u2013730 (2006)","journal-title":"Nature"},{"key":"9435_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-1542-4","volume-title":"Integral Operators in Spaces of Summable Functions","author":"M.A. Krasnoselskii","year":"1976","unstructured":"Krasnoselskii, M.A., Zabreiko, P.P., Pustylnik, E.I., Sobolevskii, P.E.: Integral Operators in Spaces of Summable Functions. Noordhoff, Leiden (1976). Translated from the Russian by T. Ando, Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics: Analysis"},{"key":"9435_CR25","series-title":"Internat. Ser. Numer. Math.","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/978-3-0348-8233-0_13","volume-title":"Fast Solution of Discretized Optimization Problems (Berlin, 2000)","author":"D. Logashenko","year":"2001","unstructured":"Logashenko, D., Maar, B., Schulz, V., Wittum, G.: Optimal geometrical design of Bingham parameter measurement devices. In: Fast Solution of Discretized Optimization Problems (Berlin, 2000). Internat. Ser. Numer. Math., vol. 138, pp. 167\u2013183. Birkh\u00e4user, Basel (2001)"},{"key":"9435_CR26","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1090\/S0002-9947-1979-0531975-1","volume":"251","author":"M. Marcus","year":"1979","unstructured":"Marcus, M., Mizel, V.J.: Complete characterization of functions which act, via superposition, on Sobolev spaces. Trans. Am. Math. Soc. 251, 187\u2013218 (1979)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9435_CR27","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/0322028","volume":"22","author":"F. Mignot","year":"1984","unstructured":"Mignot, F., Puel, J.-P.: Optimal control in some variational inequalities. SIAM J. Control Optim. 22(3), 466\u2013476 (1984)","journal-title":"SIAM J. Control Optim."},{"issue":"6","key":"9435_CR28","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1515\/RJNAMM.2008.035","volume":"23","author":"E.A. Muravleva","year":"2008","unstructured":"Muravleva, E.A., Olshanskii, M.A.: Two finite-difference schemes for calculation of Bingham fluid flows in a cavity. Russ. J. Numer. Anal. Math. Model. 23(6), 615\u2013634 (2008)","journal-title":"Russ. J. Numer. Anal. Math. Model."},{"issue":"3","key":"9435_CR29","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s002290050072","volume":"96","author":"S. Polidoro","year":"1998","unstructured":"Polidoro, S., Ragusa, M.A.: Sobolev-Morrey spaces related to an ultraparabolic equation. Manuscr. Math. 96(3), 371\u2013392 (1998)","journal-title":"Manuscr. Math."},{"issue":"1","key":"9435_CR30","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1287\/moor.18.1.227","volume":"18","author":"L.Q. Qi","year":"1993","unstructured":"Qi, L.Q.: Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18(1), 227\u2013244 (1993)","journal-title":"Math. Oper. Res."},{"issue":"11","key":"9435_CR31","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1016\/0362-546X(92)90125-X","volume":"19","author":"B.D. Reddy","year":"1992","unstructured":"Reddy, B.D.: Mixed variational inequalities arising in elastoplasticity. Nonlinear Anal. 19(11), 1071\u20131089 (1992)","journal-title":"Nonlinear Anal."},{"key":"9435_CR32","series-title":"Intl. Ser. Numer. Math.","volume-title":"Nonlinear Partial Differential Equations with Applications","author":"T. Roub\u00ed\u010dek","year":"2005","unstructured":"Roub\u00ed\u010dek, T.: Nonlinear Partial Differential Equations with Applications. Intl. Ser. Numer. Math., vol.\u00a0153. Birkh\u00e4user, Berlin (2005)"},{"key":"9435_CR33","volume-title":"Nonlinear functional analysis. An introduction. (Nichtlineare Funktionalanalysis. Eine Einf\u00fchrung.)","author":"M. Ruzicka","year":"2004","unstructured":"Ruzicka, M.: Nonlinear functional analysis. An introduction. (Nichtlineare Funktionalanalysis. Eine Einf\u00fchrung.). Springer, Berlin (2004)"},{"key":"9435_CR34","volume-title":"Navier-Stokes Equations, Theory and Numerical Analysis","author":"R. Temam","year":"1979","unstructured":"Temam, R.: Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland, Amsterdam (1979)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9435-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-011-9435-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-011-9435-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,8]],"date-time":"2021-12-08T10:21:52Z","timestamp":1638958912000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-011-9435-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,1]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9435"],"URL":"https:\/\/doi.org\/10.1007\/s10589-011-9435-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,1]]}}}