{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:12:29Z","timestamp":1775052749666,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1995,12,1]],"date-time":"1995-12-01T00:00:00Z","timestamp":817776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1995,12]]},"DOI":"10.1007\/bf01590958","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T20:06:59Z","timestamp":1114718819000},"page":"289-325","source":"Crossref","is-referenced-by-count":52,"title":["The extended linear complementarity problem"],"prefix":"10.1007","volume":"71","author":[{"given":"Bart","family":"De Schutter","sequence":"first","affiliation":[]},{"given":"Bart","family":"De Moor","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BFb0121176","volume":"31","author":"F.A. Al-Khayyal","year":"1987","unstructured":"F.A. Al-Khayyal, \u201cAn implicit enumeration procedure for the general linear complementarity problem,\u201dMathematical Programming Study 31 (1987) 1\u201320.","journal-title":"Mathematical Programming Study"},{"key":"CR2","volume-title":"Synchronization and Linearity","author":"F. Baccelli","year":"1992","unstructured":"F. Baccelli, G. Cohen, G.J. Olsder and J.P. Quadrat,Synchronization and Linearity (Wiley, New York, 1992)."},{"issue":"6","key":"CR3","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0167-6377(90)90057-C","volume":"9","author":"R. Carraghan","year":"1990","unstructured":"R. Carraghan and P.M. Pardalos, \u201cAn exact algorithm for the maximum clique problem,\u201dOperations Research Letters 9 (6) (1990) 375\u2013382.","journal-title":"Operations Research Letters"},{"issue":"3","key":"CR4","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/BF00940344","volume":"60","author":"S. Chung","year":"1989","unstructured":"S. Chung, \u201cNP-completeness of the linear complementarity problem,\u201dJournal of Optimization Theory and Applications 60 (3) (1989) 393\u2013399.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"CR5","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0021-9800(70)80010-2","volume":"8","author":"R.W. Cottle","year":"1970","unstructured":"R.W. Cottle and G.B. Dantzig, \u201cA generalization of the linear complementarity problem,\u201dJournal of Combinatorial Theory 8 (1) (1970) 79\u201390.","journal-title":"Journal of Combinatorial Theory"},{"key":"CR6","volume-title":"The Linear Complementarity Problem","author":"R.W. Cottle","year":"1992","unstructured":"R.W. Cottle, J.S. Pang and R.E. Stone,The Linear Complementarity Problem (Academic Press, Boston, 1992)."},{"key":"CR7","volume-title":"Minimax Algebra, Lecture Notes in Economics and Mathematical Systems, Vol. 166","author":"R.A. Cuninghame-Green","year":"1979","unstructured":"R.A. Cuninghame-Green,Minimax Algebra, Lecture Notes in Economics and Mathematical Systems, Vol. 166 (Springer, Berlin, 1979)."},{"key":"CR8","volume-title":"Mathematical concepts and techniques for modelling of static and dynamic systems","author":"B. Moor De","year":"1988","unstructured":"B. De Moor, \u201cMathematical concepts and techniques for modelling of static and dynamic systems,\u201d Ph.D. Thesis, Department of Electrical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium (1988)."},{"key":"CR9","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/BF01581091","volume":"57","author":"B. Moor De","year":"1992","unstructured":"B. De Moor, L. Vandenberghe and J. Vandewalle, \u201cThe generalized linear complementarity problem and an algorithm to find all its solutions,\u201dMathematical Programming 57 (1992) 415\u2013426.","journal-title":"Mathematical Programming"},{"issue":"2","key":"CR10","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0167-6911(94)00062-Z","volume":"25","author":"B. Schutter De","year":"1995","unstructured":"B. De Schutter and B. De Moor, \u201cMinimal realization in the max algebra is an extended linear complementarity problem,\u201dSystems & Control Letters 25 (2) (1995) 103\u2013111.","journal-title":"Systems & Control Letters"},{"key":"CR11","doi-asserted-by":"crossref","unstructured":"B. De Schutter and B. De Moor, \u201cA method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra,\u201dDiscrete Event Dynamic Systems: Theory and Applications, to appear.","DOI":"10.1007\/BF01797235"},{"key":"CR12","first-page":"273","volume-title":"Proceedings of the 11th International Conference on Analysis and Optimization of Systems, Sophia-Antipolis, France, Lecture Notes in Control and Information Sciences, Vol. 199","author":"B. Schutter De","year":"1994","unstructured":"B. De Schutter and B. De Moor, \u201cThe characteristic equation and minimal state space realization of SISO systems in the max algebra,\u201d in: G. Cohen and J.-P. Quadrat, eds.,Proceedings of the 11th International Conference on Analysis and Optimization of Systems, Sophia-Antipolis, France, Lecture Notes in Control and Information Sciences, Vol. 199 (Springer, New York, 1994) pp. 273\u2013282."},{"key":"CR13","first-page":"102","volume-title":"Recent Advances in Global Optimization, Princeton Series in Computer Science","author":"A.A. Ebiefung","year":"1992","unstructured":"A.A. Ebiefung and M.K. Kostreva, \u201cGlobal solvability of generalized linear complementarity problems and a related class of polynomial complementarity problems,\u201d in: C.A. Floudas and P.M. Pardalos, eds.,Recent Advances in Global Optimization, Princeton Series in Computer Science (Princeton University Press, Princeton, NJ, 1992) pp. 102\u2013124."},{"key":"CR14","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"M.R. Garey","year":"1979","unstructured":"M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, CA, 1979)."},{"key":"CR15","volume-title":"Numerical Methods for Constrained Optimization","author":"P.E. Gill","year":"1974","unstructured":"P.E. Gill and W. Murray,Numerical Methods for Constrained Optimization (Academic Press, London, 1974)."},{"issue":"3","key":"CR16","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1137\/S0895479892237859","volume":"15","author":"M.S. Gowda","year":"1994","unstructured":"M.S. Gowda and R. Sznajder, \u201cThe generalized order linear complementarity problem,\u201dSIAM Journal on Matrix Analysis and Applications 15 (3) (1994) 779\u2013795.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"CR17","doi-asserted-by":"crossref","unstructured":"M.S. Gowda, \u201cOn the extended linear complementarity problem,\u201dMathematical Programming, to appear.","DOI":"10.1007\/BF02592330"},{"issue":"4","key":"CR18","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/BF01099266","volume":"4","author":"J.J. J\u00fadice","year":"1994","unstructured":"J.J. J\u00fadice and L.N. Vicente, \u201cOn the solution and complexity of a generalized linear complementarity problem,\u201dJournal of Global Optimization 4 (4) (1994) 415\u2013424.","journal-title":"Journal of Global Optimization"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0024-3795(93)90270-X","volume":"193","author":"J.A. Kaliski","year":"1993","unstructured":"J.A. Kaliski and Y. Ye, \u201cAn extension of the potential reduction algorithm for linear complementarity problems with some priority goals,\u201dLinear Algebra and its Applications 193 (1993) 35\u201350.","journal-title":"Linear Algebra and its Applications"},{"issue":"12","key":"CR20","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1137\/S0895479893262734","volume":"16","author":"O.L. Mangasarian","year":"1995","unstructured":"O.L. Mangasarian and J.S. Pang, \u201cThe extended linear complementarity problem,\u201dSIAM Journal on Matrix Analysis and Applications 16 (12) (1995) 359\u2013368.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"2","key":"CR21","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF01585171","volume":"62","author":"O.L. Mangasarian","year":"1993","unstructured":"O.L. Mangasarian and M.V. Solodov, \u201cNonlinear complementarity as unconstrained and constrained minimization,\u201dMathematical Programming 62 (2) (1993) 277\u2013297.","journal-title":"Mathematical Programming"},{"issue":"2","key":"CR22","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1287\/moor.5.2.167","volume":"5","author":"T.H. Mattheiss","year":"1980","unstructured":"T.H. Mattheiss and D.S. Rubin, \u201cA survey and comparison of methods for finding all vertices of convex polyhedral sets,\u201dMathematics of Operations Research 5 (2) (1980) 167\u2013185.","journal-title":"Mathematics of Operations Research"},{"issue":"2","key":"CR23","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1137\/0804014","volume":"4","author":"K. McShane","year":"1994","unstructured":"K. McShane, \u201cSuperlinearly convergent $$O\\left( {\\sqrt n L} \\right)$$ -iteration interior-point algorithms for linear programming and the monotone linear complementarity problem,\u201dSIAM Journal on Optimization 4 (2) (1994) 247\u2013261.","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"CR24","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1137\/0804024","volume":"4","author":"S. Mehrotra","year":"1994","unstructured":"S. Mehrotra and R.A. Stubbs, \u201cPredictor-corrector methods for a class of linear complementarity problems,\u201dSIAM Journal on Optimization 4 (2) (1994) 441\u2013453.","journal-title":"SIAM Journal on Optimization"},{"key":"CR25","first-page":"51","volume-title":"Contributions to the Theory of Games, Annals of Mathematics Studies, Vol. 28","author":"T.S. Motzkin","year":"1953","unstructured":"T.S. Motzkin, H. Raiffa, G.L. Thompson and R.M. Thrall, \u201cThe double description method,\u201d in: H.W. Kuhn and A.W. Tucker, eds.,Contributions to the Theory of Games, Annals of Mathematics Studies, Vol. 28 (Princeton University Press, Princeton, NJ, 1953) pp. 51\u201373."},{"key":"CR26","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0000035","volume-title":"Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science, Vol. 268","author":"P.M. Pardalos","year":"1987","unstructured":"P.M. Pardalos and J.B. Rosen,Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science, Vol. 268 (Springer, Berlin, 1987)."},{"key":"CR27","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/BF01098364","volume":"4","author":"P.M. Pardalos","year":"1994","unstructured":"P.M. Pardalos and J. Xue, \u201cThe maximum clique problem,\u201dJournal of Global Optimization 4 (1994) 301\u2013328.","journal-title":"Journal of Global Optimization"},{"key":"CR28","volume-title":"Theory of Linear and Integer Programming","author":"A. Schrijver","year":"1986","unstructured":"A. Schrijver,Theory of Linear and Integer Programming (Wiley, Chichester, 1986)."},{"key":"CR29","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/0022-247X(89)90347-8","volume":"144","author":"M. Sun","year":"1989","unstructured":"M. Sun, \u201cMonotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems,\u201dJournal of Mathematical Analysis and Applications 144 (1989) 474\u2013485.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"CR30","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/0024-3795(93)00184-2","volume":"223\u2013224","author":"R. Sznajder","year":"1995","unstructured":"R. Sznajder and M.S. Gowda, \u201cGeneralizations ofP 0- andP-properties; extended vertical and horizontal LCPs,\u201dLinear Algebra and its Applications 223\u2013224 (1995) 695\u2013716.","journal-title":"Linear Algebra and its Applications"},{"key":"CR31","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/0024-3795(94)00147-6","volume":"223\u2013224","author":"R.H. T\u00fct\u00fcnc\u00fc","year":"1995","unstructured":"R.H. T\u00fct\u00fcnc\u00fc and M.J. Todd, \u201cReducing horizontal linear complementarity problems,\u201dLinear Algebra and its Application 223\u2013224 (1995) 717\u2013730.","journal-title":"Linear Algebra and its Application"},{"issue":"11","key":"CR32","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1109\/31.41295","volume":"36","author":"L. Vandenberghe","year":"1989","unstructured":"L. Vandenberghe, B. De Moor and J. Vandewalle, \u201cThe generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits,\u201dIEEE Transactions on Circuits and Systems 36 (11) (1989) 1382\u20131391.","journal-title":"IEEE Transactions on Circuits and Systems"},{"issue":"2","key":"CR33","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1287\/moor.18.2.334","volume":"18","author":"Y. Ye","year":"1993","unstructured":"Y. Ye, \u201cA fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem,\u201dMathematics of Operations Research 18 (2) (1993) 334\u2013345.","journal-title":"Mathematics of Operations Research"},{"issue":"1","key":"CR34","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1137\/0804012","volume":"4","author":"Y. Zhang","year":"1994","unstructured":"Y. Zhang, \u201cOn the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem,\u201dSIAM Journal on Optimization 4 (1) (1994) 208\u2013227.","journal-title":"SIAM Journal on Optimization"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/BF01590958.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/article\/10.1007\/BF01590958\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/BF01590958","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T15:42:54Z","timestamp":1556898174000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/http\/link.springer.com\/10.1007\/BF01590958"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["BF01590958"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1007\/bf01590958","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}