{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:09:44Z","timestamp":1758823784893},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T00:00:00Z","timestamp":1173312000000},"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":[[2007,3,29]]},"DOI":"10.1007\/s10589-007-9013-4","type":"journal-article","created":{"date-parts":[[2007,3,7]],"date-time":"2007-03-07T12:56:22Z","timestamp":1173272182000},"page":"67-81","source":"Crossref","is-referenced-by-count":7,"title":["Solving variational inequalities defined on a domain with infinitely many linear constraints"],"prefix":"10.1007","volume":"37","author":[{"given":"Shu-Cherng","family":"Fang","sequence":"first","affiliation":[]},{"given":"Soonyi","family":"Wu","sequence":"additional","affiliation":[]},{"given":"\u015e. \u0130lker","family":"Birbil","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,3,8]]},"reference":[{"key":"9013_CR1","volume-title":"Linear Programming in Infinite-Dimensional Spaces","author":"E.J. Anderson","year":"1987","unstructured":"Anderson, E.J., Nash, P.: Linear Programming in Infinite-Dimensional Spaces. Wiley, Chichester (1987)"},{"key":"9013_CR2","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1023\/A:1022452626305","volume":"25","author":"S.I. Birbil","year":"2003","unstructured":"Birbil, S.I., Fang, S.-C.: An electromagnetism-like mechanism for global optimization. J. Glob. Optim. 25, 263\u2013282 (2003)","journal-title":"J. Glob. Optim."},{"key":"9013_CR3","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01386389","volume":"1","author":"E.W. Cheney","year":"1959","unstructured":"Cheney, E.W., Goldstein, A.A.: Newton\u2019s method for convex programming and Tchebycheff approximation. Numer. Math. 1, 253\u2013268 (1959)","journal-title":"Numer. Math."},{"key":"9013_CR4","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1137\/0309037","volume":"9","author":"B.C. Eaves","year":"1971","unstructured":"Eaves, B.C., Zangwill, W.I.: Generalized cutting plane algorithms. SIAM J. Control 9, 529\u2013542 (1971)","journal-title":"SIAM J. Control"},{"key":"9013_CR5","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/BF01580439","volume":"8","author":"J. Elzinga","year":"1975","unstructured":"Elzinga, J., Moore, T.G.: A central cutting plane algorithm for the convex programming problem. Math. Program. 8, 134\u2013145 (1975)","journal-title":"Math. Program."},{"key":"9013_CR6","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F. Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)"},{"key":"9013_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6131-6","volume-title":"Entropy Optimization and Mathematical Programming","author":"S.-C. Fang","year":"1997","unstructured":"Fang, S.-C., Rajasekera, J.R., Tsao, H.-S.J.: Entropy Optimization and Mathematical Programming. Kluwer Academic, Boston (1997)"},{"key":"9013_CR8","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1023\/B:JOGO.0000015308.49676.ea","volume":"28","author":"S.-C. Fang","year":"2004","unstructured":"Fang, S.-C., Wu, S.-Y., Sun, J.: An analytic center cutting plane method for solving semi-infinite variational inequality problems. J. Glob. Optim. 28, 141\u2013152 (2004)","journal-title":"J. Glob. Optim."},{"key":"9013_CR9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-1-4757-2868-2_1","volume-title":"Semi-Infinite Programming","author":"M.A. Goberna","year":"1998","unstructured":"Goberna, M.A., Lopez, M.A.: A comprehensive survey of linear semi-infinite optimization theory. In: Reemsten, R., Ruckmann, J.-J. (eds.) Semi-Infinite Programming, pp.\u00a03\u201327. Kluwer Academic, Dordrecht (1998)"},{"key":"9013_CR10","volume-title":"Large Scale Optimization: State of the Art","author":"J.-L. Goffin","year":"1993","unstructured":"Goffin, J.-L., Luo, Z.-Q., Ye, Y.: On the complexity of a column generation algorithm for convex or quasiconvex feasibility problems. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds.) Large Scale Optimization: State of the Art. Kluwer, New York (1993)"},{"key":"9013_CR11","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1137\/S1052623493258635","volume":"6","author":"J.-L. Goffin","year":"1996","unstructured":"Goffin, J.-L., Luo, Z., Ye, Y.: Complexity analysis of an interior cutting plane method for convex feasibility problems. SIAM J. Optim. 6, 638\u2013652 (1996)","journal-title":"SIAM J. Optim."},{"key":"9013_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-6377(96)00029-6","volume":"20","author":"J.-L. Goffin","year":"1997","unstructured":"Goffin, J.-L., Marcotte, P., Zhu, D.: An analytic center cutting plane method for pseudomonotone variational inequalities. Oper. Res. Lett. 20, 1\u20136 (1997)","journal-title":"Oper. Res. Lett."},{"key":"9013_CR13","unstructured":"Goffin, J.-L., Vial, J.-P.: Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method, Logilab Technical report, Department of Management Studies, University of Geneva, Switzerland (1999)"},{"key":"9013_CR14","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1023\/B:JOTA.0000042593.74934.b7","volume":"122","author":"J. Han","year":"2004","unstructured":"Han, J., Huang, Z.-H., Fang, S.-C.: Solvability of variational inequality problems. J. Optim. Theory Appl. 122, 501\u2013520 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9013_CR15","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"Harker, P.T., Pang, J.-S.: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. 48, 161\u2013220 (1990)","journal-title":"Math. Program."},{"key":"9013_CR16","first-page":"703","volume":"8","author":"R. Horst","year":"1960","unstructured":"Horst, R.: Deterministic methods in constrained global optimization: some recent advances and new fields of application. J. SIAM 8, 703\u2013712 (1960)","journal-title":"J. SIAM"},{"key":"9013_CR17","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01386389","volume":"1","author":"J.E. Kelley","year":"1959","unstructured":"Kelley, J.E.: The cutting-plane method for solving convex programs. Numer. Math. 1, 253\u2013268 (1959)","journal-title":"Numer. Math."},{"key":"9013_CR18","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1137\/S1052623495294943","volume":"9","author":"Z.-Q. Luo","year":"1999","unstructured":"Luo, Z.-Q., Sun, J.: An analytic center based column generation algorithm for convex quadratic feasibility problems. SIAM J. Optim. 9, 217\u2013235 (1999)","journal-title":"SIAM J. Optim."},{"key":"9013_CR19","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1023\/A:1008787027641","volume":"15","author":"Z.-Q. Luo","year":"2000","unstructured":"Luo, Z.-Q., Sun, J.: A polynomial cutting surfaces algorithm for the convex feasibility problem defined by self-concordant inequalities. Comput. Optim. Appl. 15, 167\u2013191 (2000)","journal-title":"Comput. Optim. Appl."},{"key":"9013_CR20","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1137\/S1052623498338321","volume":"10","author":"H.-J. L\u00fcthi","year":"2000","unstructured":"L\u00fcthi, H.-J., Bueler, B.: An analytical center quadratic cut method for strongly monotone variational inequality problems. SIAM J. Optim. 10, 415\u2013426 (2000)","journal-title":"SIAM J. Optim."},{"key":"9013_CR21","first-page":"327","volume":"71","author":"T.L. Magnanti","year":"1995","unstructured":"Magnanti, T.L., Perakis, G.: A unifying geometric solution framework and complexity analysis for variational inequalities. Math. Program. 71, 327\u2013351 (1995)","journal-title":"Math. Program."},{"key":"9013_CR22","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1023\/A:1011219303531","volume":"20","author":"P. Marcotte","year":"2001","unstructured":"Marcotte, P., Zhu, D.: A cutting plane method for solving quasimonotone variational inequalities. Comput. Optim. Appl. 20, 317\u2013324 (2001)","journal-title":"Comput. Optim. Appl."},{"key":"9013_CR23","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1137\/S1052623497324813","volume":"9","author":"Yu. Nesterov","year":"1999","unstructured":"Nesterov, Yu., Vial, J.-Ph.: Homogeneous analytic center cutting plane methods for convex problems and variational inequalities. SIAM J. Optim. 9, 708\u2013728 (1999)","journal-title":"SIAM J. Optim."},{"key":"9013_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2868-2","volume-title":"Semi-Infinite Programming","author":"R. Reemtsen","year":"1998","unstructured":"Reemtsen, R., Ruckmann, J.-J. (eds.): Semi-Infinite Programming. Kluwer Academic, Dordrecht (1998)"},{"key":"9013_CR25","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/978-1-4757-2868-2_7","volume-title":"Semi-Infinite Programming","author":"R. Reemtsen","year":"1998","unstructured":"Reemtsen, R., Ruckmann, J.-J.: Numerical methods for semi-infinite programming: a survey. In: Reemsten, R., Ruckmann, J.-J. (eds.) Semi-Infinite Programming, pp.\u00a0195\u2013275. Kluwer Academic, Dordrecht (1998)"},{"key":"9013_CR26","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1080\/02331938808843393","volume":"19","author":"R. Tichatschke","year":"1988","unstructured":"Tichatschke, R., Nobeling, V.: A cutting plane method for quadratic semi-infinite programming problems. Optimization 19, 803\u2013817 (1988)","journal-title":"Optimization"},{"key":"9013_CR27","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1287\/opre.15.1.147","volume":"15","author":"A.F. Veinott","year":"1967","unstructured":"Veinott, A.F.: The supporting hyperplane method for unimodal programming. Oper. Res. 15, 147\u2013152 (1967)","journal-title":"Oper. Res."},{"key":"9013_CR28","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1023\/A:1021763419562","volume":"99","author":"S.-Y. Wu","year":"1998","unstructured":"Wu, S.-Y., Fang, S.-C., Lin, C.-J.: Relaxed cutting plane method for solving linear semi-infinite programming problems. J. Optim. Theory Appl. 99, 759\u2013779 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"9013_CR29","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1023\/A:1008202323884","volume":"14","author":"Y.B. Zhao","year":"1998","unstructured":"Zhao, Y.B., Han, J.: Exceptional family of elements for variational inequality problem and its applications. J. Glob. Optim. 14, 313\u2013330 (1998).","journal-title":"J. Glob. Optim."},{"key":"9013_CR30","first-page":"25","volume":"16","author":"Y.J. Zhu","year":"1966","unstructured":"Zhu, Y.J.: Generalization of some fundamental theorems on linear inequalities. Acta Math. Sinica 16, 25\u201340 (1966)","journal-title":"Acta Math. Sinica"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9013-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-007-9013-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-007-9013-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:31Z","timestamp":1559288191000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-007-9013-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3,8]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,3,29]]}},"alternative-id":["9013"],"URL":"https:\/\/doi.org\/10.1007\/s10589-007-9013-4","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3,8]]}}}