{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:27:09Z","timestamp":1761611229986},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,9,16]],"date-time":"2008-09-16T00:00:00Z","timestamp":1221523200000},"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":[[2010,7]]},"DOI":"10.1007\/s10589-008-9201-x","type":"journal-article","created":{"date-parts":[[2008,9,15]],"date-time":"2008-09-15T16:46:39Z","timestamp":1221497199000},"page":"535-569","source":"Crossref","is-referenced-by-count":7,"title":["A shape and topology optimization technique for\u00a0solving a class of linear complementarity problems in\u00a0function space"],"prefix":"10.1007","volume":"46","author":[{"given":"M.","family":"Hinterm\u00fcller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Laurain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,9,16]]},"reference":[{"key":"9201_CR1","series-title":"Van Nostrand Mathematical Study","volume-title":"Lectures on Elliptic Boundary Value Problems","author":"S. Agmon","year":"1965","unstructured":"Agmon, S.: Lectures on Elliptic Boundary Value Problems. Van Nostrand Mathematical Study, vol.\u00a02. Van Nostrand, Toronto (1965)"},{"issue":"1","key":"9201_CR2","first-page":"117","volume":"34","author":"M. Dambrine","year":"2005","unstructured":"Dambrine, M., Vial, G.: On the influence of a boundary perforation on the Dirichlet energy. Control Cybern. 34(1), 117\u2013136 (2005)","journal-title":"Control Cybern."},{"key":"9201_CR3","series-title":"SIAM Advances in Design and Control","volume-title":"Shapes and Geometries. Analysis, Differential Calculus and Optimization","author":"M. Delfour","year":"2001","unstructured":"Delfour, M., Zolesio, J.-P.: Shapes and Geometries. Analysis, Differential Calculus and Optimization. SIAM Advances in Design and Control. SIAM, Philadelphia (2001)"},{"key":"9201_CR4","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1007\/BF01742933","volume":"8","author":"H. Eschenauer","year":"1994","unstructured":"Eschenauer, H., Schumacher, A.: Bubble method for topology and shape optimization of structures. Struct. Optim. 8, 42\u201351 (1994)","journal-title":"Struct. Optim."},{"key":"9201_CR5","doi-asserted-by":"crossref","first-page":"1756","DOI":"10.1137\/S0363012900369538","volume":"39","author":"S. Garreau","year":"2001","unstructured":"Garreau, S., Guillaume, P., Masmoudi, M.: The topological asymptotic for pde systems: the elasticity case. SIAM J. Control Optim. 39, 1756\u20131778 (2001)","journal-title":"SIAM J. Control Optim."},{"key":"9201_CR6","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-11490-8","volume-title":"Elliptic Differential Equations","author":"W. Hackbusch","year":"1992","unstructured":"Hackbusch, W.: Elliptic Differential Equations. Springer Series in Computational Mathematics, vol. 18. Springer, Berlin (1992)"},{"key":"9201_CR7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF01400918","volume":"42","author":"W. Hackbusch","year":"1983","unstructured":"Hackbusch, W., Mittelmann, H.: On multigrid methods for variational inequalities. Numer. Math. 42, 65\u201376 (1983)","journal-title":"Numer. Math."},{"issue":"1","key":"9201_CR8","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1137\/040611598","volume":"17","author":"M. Hinterm\u00fcller","year":"2006","unstructured":"Hinterm\u00fcller, M., Kunisch, K.: Path-following methods for a class of constrained minimization problems in function space. SIAM J. Optim. 17(1), 159\u2013187 (2006)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"9201_CR9","doi-asserted-by":"crossref","first-page":"1198","DOI":"10.1137\/050637480","volume":"45","author":"M. Hinterm\u00fcller","year":"2006","unstructured":"Hinterm\u00fcller, M., Kunisch, K.: Feasible and non-interior path-following in constrained minimization with low multiplier regularity. SIAM J. Control Optim. 45(4), 1198\u20131221 (2006)","journal-title":"SIAM J. Control Optim."},{"key":"9201_CR10","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s00211-004-0531-z","volume":"98","author":"M. Hinterm\u00fcller","year":"2004","unstructured":"Hinterm\u00fcller, M., Ring, W.: A level set approach for the solution of a state-constrained optimal control problem. Numer. Math. 98, 135\u2013166 (2004)","journal-title":"Numer. Math."},{"key":"9201_CR11","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-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13, 865\u2013888 (2003)","journal-title":"SIAM J. Optim."},{"key":"9201_CR12","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.1137\/0724069","volume":"24","author":"R.H.W. Hoppe","year":"1987","unstructured":"Hoppe, R.H.W.: Multigrid methods for variational inequalities. SIAM J. Numer. Anal. 24, 1046\u20131065 (1987)","journal-title":"SIAM J. Numer. Anal."},{"key":"9201_CR13","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1080\/02331938708843301","volume":"18","author":"R.H.W. Hoppe","year":"1987","unstructured":"Hoppe, R.H.W.: Two-sided approximations for unilateral variational inequalities by multigrid methods. Optimization 18, 867\u2013881 (1987)","journal-title":"Optimization"},{"key":"9201_CR14","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1137\/0731016","volume":"31","author":"R.H.W. Hoppe","year":"1994","unstructured":"Hoppe, R.H.W., Kornhuber, R.: Adaptive multilevel methods for obstacle problems. SIAM J. Numer. Anal. 31, 301\u2013323 (1994)","journal-title":"SIAM J. Numer. Anal."},{"key":"9201_CR15","volume-title":"An Introduction to Variational Inequalities and Their Applications","author":"D. Kinderlehrer","year":"1980","unstructured":"Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic, New York (1980)"},{"key":"9201_CR16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BF03325426","volume":"69","author":"R. Kornhuber","year":"1994","unstructured":"Kornhuber, R.: Monotone multigrid methods for elliptic variational inequalities I. Numer. Math. 69, 167\u2013184 (1994)","journal-title":"Numer. Math."},{"key":"9201_CR17","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s002110050178","volume":"72","author":"R. Kornhuber","year":"1996","unstructured":"Kornhuber, R.: Monotone multigrid methods for elliptic variational inequalities II. Numer. Math. 72, 481\u2013499 (1996)","journal-title":"Numer. Math."},{"key":"9201_CR18","volume-title":"Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems","author":"R. Kornhuber","year":"1997","unstructured":"Kornhuber, R.: Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems. Teubner, Stuttgart (1997)"},{"key":"9201_CR19","volume-title":"Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains","author":"V. Maz\u2019ya","year":"2000","unstructured":"Maz\u2019ya, V., Nazarov, S.A., Plamenevskij, B.: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vols. 1, 2. Birkh\u00e4user, Basel (2000)"},{"key":"9201_CR20","volume-title":"Level Set Methods and Dynamic Implicit Surfaces","author":"S. Osher","year":"2004","unstructured":"Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2004)"},{"key":"9201_CR21","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. Osher","year":"1988","unstructured":"Osher, S., Sethian, J.: Fronts propagating with curvature-dependant speed: algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"9201_CR22","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1006\/jcph.1999.6345","volume":"155","author":"D. Peng","year":"1999","unstructured":"Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A pde-based fast local level set method. J.\u00a0Comput. Phys. 155, 410\u2013438 (1999)","journal-title":"J.\u00a0Comput. Phys."},{"key":"9201_CR23","volume-title":"Level Set Methods and Fast Marching Methods","author":"J.A. Sethian","year":"1999","unstructured":"Sethian, J.A.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)","edition":"2"},{"key":"9201_CR24","volume-title":"Numerical Solution of Partial Differential Equations: Finite Difference Methods","author":"G.D. Smith","year":"1993","unstructured":"Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon, Oxford (1993)"},{"issue":"4","key":"9201_CR25","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1137\/S0363012997323230","volume":"37","author":"J. Sokolowski","year":"1999","unstructured":"Sokolowski, J., Zochowski, A.: On the topological derivative in shape optimization. SIAM J. Control Optim. 37(4), 1251\u20131272 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"9201_CR26","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58106-9","volume-title":"Introduction to Shape Optimization","author":"J. Sokolowski","year":"1992","unstructured":"Sokolowski, J., Zolesio, J.-P.: Introduction to Shape Optimization. Springer Series in Computational Mathematics, vol. 16. Springer, Berlin (1992)"},{"key":"9201_CR27","first-page":"233","volume":"9","author":"X.-C. Tai","year":"2001","unstructured":"Tai, X.-C.: Convergence rate analysis of domain decomposition methods for obstacle problems. East-West J. Numer. Math. 9, 233\u2013252 (2001)","journal-title":"East-West J. Numer. Math."},{"key":"9201_CR28","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1007\/s002110200404","volume":"93","author":"X.-C. Tai","year":"2003","unstructured":"Tai, X.-C.: Rate of convergence for some constraint decomposition methods for nonlinear variational inequalities. Numer. Math. 93, 755\u2013786 (2003)","journal-title":"Numer. Math."},{"key":"9201_CR29","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1090\/S0025-5718-01-01344-8","volume":"71","author":"X.-C. Tai","year":"2001","unstructured":"Tai, X.-C., Tseng, P.: Convergence rate analysis of an asynchronous space decomposition method for convex minimization. Math. Comput. 71, 1105\u20131135 (2001)","journal-title":"Math. Comput."},{"key":"9201_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-96662-9","volume-title":"Partielle Differentialgleichungen","author":"J. Wloka","year":"1982","unstructured":"Wloka, J.: Partielle Differentialgleichungen. Teubner, Stuttgart (1982)"},{"key":"9201_CR31","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1006\/jcph.1996.0167","volume":"122","author":"H.K. Zhao","year":"1996","unstructured":"Zhao, H.K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multi-phase motion. J. Comput. Phys. 122, 179\u2013195 (1996)","journal-title":"J. Comput. Phys."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9201-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-008-9201-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9201-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:35Z","timestamp":1559302595000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-008-9201-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,16]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,7]]}},"alternative-id":["9201"],"URL":"https:\/\/doi.org\/10.1007\/s10589-008-9201-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,16]]}}}