{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T06:05:44Z","timestamp":1780639544465,"version":"3.54.1"},"reference-count":28,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research Letters"],"published-print":{"date-parts":[[2000,9]]},"DOI":"10.1016\/s0167-6377(00)00042-0","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T10:32:20Z","timestamp":1027593140000},"page":"83-91","source":"Crossref","is-referenced-by-count":38,"title":["Projected dynamical systems in a complementarity formalism"],"prefix":"10.1016","volume":"27","author":[{"given":"W.P.M.H.","family":"Heemels","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.M.","family":"Schumacher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Weiland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/S0167-6377(00)00042-0_BIB1","doi-asserted-by":"crossref","DOI":"10.1109\/TAC.1998.664148","article-title":"Special issue on hybrid control systems","volume":"43","author":"Antsaklis","year":"1998","journal-title":"IEEE Trans. Automa. Control"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB2","series-title":"Piecewise Linear Modelling and Analysis","author":"van Bokhoven","year":"1981"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB3","unstructured":"M.K. \u00c7aml\u0131bel, W.P.M.H. Heemels, J.M. Schumacher, Dynamical analysis of linear passive networks with ideal diodes, Part II: consistency of a time-stepping method, Technical Report 00 I\/03, Eindhoven University of Technology, Department of Electrical Engineering, Measurement and Control Systems, Eindhoven, The Netherlands, 2000."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB4","series-title":"The Linear Complementarity Problem","author":"Cottle","year":"1992"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB5","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1080\/17442508708833451","article-title":"Large deviations analysis of reflected diffusions and constrained stochastic approximation algorithms in convex sets","volume":"21","author":"Dupuis","year":"1987","journal-title":"Stochastics"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB6","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02073589","article-title":"Dynamical systems and variational inequalities","volume":"44","author":"Dupuis","year":"1993","journal-title":"Ann. Oper. Res."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB7","unstructured":"A.F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb 51 (1960) 99\u2013128 (in Russian) (English translation: Am. Math. Soc. Transl. 62 (1964))."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB8","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","article-title":"Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications","volume":"48","author":"Harker","year":"1990","journal-title":"Math. Programming Ser. B"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB9","unstructured":"W.P.M.H. Heemels, Linear complementarity systems: a study in hybrid dynamics, Ph.D. Dissertation, Eindhoven University of Technology, Department of Electrical Engineering, Eindhoven, The Netherlands, 1999."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB10","unstructured":"W.P.M.H. Heemels, M.K. \u00c7aml\u0131bel, J.M. Schumacher, Dynamical analysis of linear passive networks with ideal diodes, Part I: well-posedness, Technical Report 00 I\/02, Eindhoven University of Technology, Dept. of Electrical Engineering, Measurement and Control Systems, Eindhoven, The Netherlands, 2000."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB11","doi-asserted-by":"crossref","unstructured":"W.P.M.H. Heemels, J.M. Schumacher, S. Weiland, Applications of complementarity systems, Proceedings of the European Control Conference, Karlsruhe, Germany, 1999.","DOI":"10.23919\/ECC.1999.7099808"},{"issue":"1\u20133","key":"10.1016\/S0167-6377(00)00042-0_BIB12","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0024-3795(99)00060-9","article-title":"The rational complementarity problem","volume":"294","author":"Heemels","year":"1999","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"10.1016\/S0167-6377(00)00042-0_BIB13","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1137\/S0036139997325199","article-title":"Linear complementarity systems","volume":"60","author":"Heemels","year":"2000","journal-title":"SIAM J. Appl. Math."},{"issue":"3","key":"10.1016\/S0167-6377(00)00042-0_BIB14","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/S0005-1098(98)90177-7","article-title":"Uniqueness of solutions of relay systems","volume":"35","author":"Lootsma","year":"1999","journal-title":"Automatica"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB15","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1137\/0142022","article-title":"Mechanical systems of rigid bodies subject to unilateral constraints","volume":"42","author":"L\u00f6tstedt","year":"1982","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB16","series-title":"Optimization by Vector Space Methods","author":"Luenberger","year":"1969"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB17","first-page":"238","article-title":"D\u00e9composition orthogonale d'un espace hilbertien selon deux c\u00f4nes mutuellement p\u00f4laires","volume":"255","author":"Moreau","year":"1962","journal-title":"C.R. Acad. Sci. Paris"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB18","series-title":"Projected Dynamical Systems and Variational Inequalities with Applications","author":"Nagurney","year":"1996"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB19","series-title":"Multibody Dynamics with Unilateral Contacts","author":"Pfeiffer","year":"1996"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB20","doi-asserted-by":"crossref","unstructured":"A. Pnueli, J. Sifakis (Guest Eds.), Special issue on hybrid systems, Theoret. Comput. Sci. 138 (1995).","DOI":"10.1016\/0304-3975(95)90065-9"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB21","series-title":"Convex Analysis","author":"Rockafellar","year":"1970"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB22","series-title":"Principles of Mathematical Analysis","author":"Rudin","year":"1976"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB23","series-title":"System Theoretic Descriptions of Physical Systems, CWI Tract 3","author":"van der Schaft","year":"1984"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB24","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1007\/BF02551330","article-title":"The complementary-slackness class of hybrid systems","volume":"9","author":"van der Schaft","year":"1996","journal-title":"Math. Control Signals Systems"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB25","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1109\/9.664151","article-title":"Complementarity modelling of hybrid systems","volume":"43","author":"van der Schaft","year":"1998","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB26","doi-asserted-by":"crossref","unstructured":"A.J. van der Schaft, J.M. Schumacher, An Introduction to Hybrid Dynamical Systems, Lecture Notes in Control and Information Sciences, Vol. 251, Springer, London, 2000.","DOI":"10.1007\/BFb0109998"},{"key":"10.1016\/S0167-6377(00)00042-0_BIB27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0024-3795(99)00004-X","article-title":"Eigenvalue analysis of equilibrium processes defined by linear complementarity conditions","volume":"292","author":"Seeger","year":"1999","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0167-6377(00)00042-0_BIB28","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1137\/1106035","article-title":"Stochastic equations for diffusions in a bounded region","volume":"6","author":"Skorokhod","year":"1961","journal-title":"Theory Probab. Appl."}],"container-title":["Operations Research Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167637700000420?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167637700000420?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T06:08:59Z","timestamp":1578550139000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167637700000420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S0167637700000420"],"URL":"https:\/\/doi.org\/10.1016\/s0167-6377(00)00042-0","relation":{},"ISSN":["0167-6377"],"issn-type":[{"value":"0167-6377","type":"print"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}