{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T23:04:55Z","timestamp":1648595095968},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"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":[[2011,7]]},"DOI":"10.1007\/s10589-009-9309-7","type":"journal-article","created":{"date-parts":[[2009,11,30]],"date-time":"2009-11-30T20:29:44Z","timestamp":1259612984000},"page":"493-520","source":"Crossref","is-referenced-by-count":3,"title":["A new hybrid method for nonlinear complementarity problems"],"prefix":"10.1007","volume":"49","author":[{"given":"Shao-Jian","family":"Qu","sequence":"first","affiliation":[]},{"given":"Mark","family":"Goh","sequence":"additional","affiliation":[]},{"given":"Xiujie","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,12,1]]},"reference":[{"key":"9309_CR1","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1137\/S0036144595285963","volume":"39","author":"M.C. Ferris","year":"1997","unstructured":"Ferris, M.C., Pang, J.S.: Engineering and economic applications of complementarity problems. SIAM Rev. 39, 669\u2013713 (1997)","journal-title":"SIAM Rev."},{"key":"9309_CR2","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/978-1-4899-0289-4_11","volume-title":"Nonlinear Optimization and Applications","author":"M. Fukushima","year":"1996","unstructured":"Fukushima, M.: Merit functions for variational inequality and complementarity problems. In: Di\u00a0Pillo, G., Giannessi, F. (eds.) Nonlinear Optimization and Applications, pp. 155\u2013170. Plenum, New York (1996)"},{"key":"9309_CR3","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 Appl. Math. Program. 48, 161\u2013220 (1990)","journal-title":"Math. Program."},{"key":"9309_CR4","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/978-1-4615-2025-2_6","volume-title":"Handbook of Global Optimization","author":"J.S. Pang","year":"1995","unstructured":"Pang, J.S.: Complementarity problems. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization, pp. 271\u2013338. Kluwer Academic, Boston (1995)"},{"issue":"2","key":"9309_CR5","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/10556780500397074","volume":"22","author":"J.W. Zhang","year":"2007","unstructured":"Zhang, J.W., Li, D.H.: A norm descent BFGS method for solving KKT systems of symmetric variational inequality problems. Optim. Methods Softw. 22(2), 237\u2013252 (2007)","journal-title":"Optim. Methods Softw."},{"key":"9309_CR6","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s10479-004-5026-x","volume":"133","author":"Y.F. Yang","year":"2005","unstructured":"Yang, Y.F., Qi, L.Q.: Smoothing trust region methods for nonlinear complementarity problems with P 0-functions. Ann. Oper. Res. 133, 99\u2013117 (2005)","journal-title":"Ann. Oper. Res."},{"key":"9309_CR7","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/S0453-4514(00)88750-5","volume":"43","author":"X. Chen","year":"2000","unstructured":"Chen, X.: Smoothing methods for complementarity problems and their applications: a survey. J. Oper. Res. Soc. Jpn. 43, 32\u201347 (2000)","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"9309_CR8","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1137\/S1052623494279110","volume":"7","author":"F. Facchinei","year":"1997","unstructured":"Facchinei, F., Soares, J.: A new merit function for nonlinear complementarity problems and a related algorithm. SIAM J. Optim. 7, 225\u2013247 (1997)","journal-title":"SIAM J. Optim."},{"key":"9309_CR9","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1080\/02331939208843795","volume":"24","author":"A. Fischer","year":"1992","unstructured":"Fischer, A.: A special Newton-type optimization method. Optimization 24, 269\u2013284 (1992)","journal-title":"Optimization"},{"key":"9309_CR10","first-page":"513","volume":"76","author":"A. Fischer","year":"1997","unstructured":"Fischer, A.: Solution of monotone complementarity problems with locally Lipschitzian functions. Math. Program. 76, 513\u2013532 (1997)","journal-title":"Math. Program."},{"key":"9309_CR11","first-page":"105","volume-title":"Complementarity and Variational Problems: State of the Art","author":"S.A. Gabriel","year":"1997","unstructured":"Gabriel, S.A., Mor, J.J.: Smoothing of mixed complementarity problems. In: Ferris, M.C., Pang, J.S. (eds.) Complementarity and Variational Problems: State of the Art, pp. 105\u2013116. SIAM, Philadelphia (1997)"},{"key":"9309_CR12","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1137\/S0895479894273134","volume":"17","author":"C. Kanzow","year":"1996","unstructured":"Kanzow, C.: Some noninterior continuation methods for linear complementarity problems. SIAM J. Matrix Anal. Appl. 17, 851\u2013868 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9309_CR13","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1137\/S1052623497324047","volume":"10","author":"H. Qi","year":"2000","unstructured":"Qi, H.: A regularized smoothing Newton method for box constrained variational inequality problems with P0-functions. SIAM J. Optim. 10, 315\u2013330 (2000)","journal-title":"SIAM J. Optim."},{"key":"9309_CR14","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02591998","volume":"29","author":"M.J.D. Powell","year":"1984","unstructured":"Powell, M.J.D.: On the global convergence of trust region algorithms for unconstrained optimization. Math. Program. 29, 297\u2013303 (1984)","journal-title":"Math. Program."},{"key":"9309_CR15","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1137\/0722003","volume":"22","author":"G.A. Schultz","year":"1985","unstructured":"Schultz, G.A., Schnabel, R.B., Byrd, R.H.: A family of trust region based algorithms for unconstrained minimization with strong global convergence. SIAM J. Numer. Anal. 22, 47\u201367 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"9309_CR16","first-page":"333","volume":"16","author":"Y. Yuan","year":"1996","unstructured":"Yuan, Y.: On the convergence of trust region algorithms. Math. Numer. Sin. 16, 333\u2013346 (1996)","journal-title":"Math. Numer. Sin."},{"key":"9309_CR17","volume-title":"Optimization Theory and Methods","author":"Y. Yuan","year":"1997","unstructured":"Yuan, Y., Sun, W.: Optimization Theory and Methods. Science Press, Beijing (1997)"},{"key":"9309_CR18","unstructured":"Nocedal, J., Yuan, Y.: Combining trust region and line search techniques. Report NAM 07, Department of EECS, Northwestern University (1991)"},{"key":"9309_CR19","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0717023","volume":"17","author":"W.C. Davidon","year":"1980","unstructured":"Davidon, W.C.: Conic approximation and collinear scaling for optimizers. SIAM J. Numer. Anal. 17, 268\u2013281 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"9309_CR20","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1137\/0717011","volume":"17","author":"D.C. Sorensen","year":"1980","unstructured":"Sorensen, D.C.: The q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. SIAM J. Numer. Anal. 17, 84\u2013114 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"9309_CR21","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF02238081","volume":"54","author":"S. Sheng","year":"1995","unstructured":"Sheng, S.: Interpolation by conic model for unconstrained optimization. Computing 54, 83\u201398 (1995)","journal-title":"Computing"},{"key":"9309_CR22","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.amc.2006.05.057","volume":"183","author":"Y. Ji","year":"2006","unstructured":"Ji, Y., Qu, S.J., Wang, Y.J., Li, H.M.: A conic trust-region method for optimization with nonlinear equality and inequality constrains via active-set strategy. Appl. Math. Comput. 183, 217\u2013231 (2006)","journal-title":"Appl. Math. Comput."},{"key":"9309_CR23","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/10556789608805637","volume":"6","author":"S. Di","year":"1996","unstructured":"Di, S., Sun, W.: Trust region method for conic model to solve unconstrained optimization problems. Optim. Methods Softw. 6, 237\u2013263 (1996)","journal-title":"Optim. Methods Softw."},{"issue":"3","key":"9309_CR24","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1137\/S1052623402418991","volume":"15","author":"Q. Ni","year":"2005","unstructured":"Ni, Q.: Optimality conditions for trust region subproblems involving a conic model. SIAM J. Optim. 15(3), 826\u2013837 (2005)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"9309_CR25","first-page":"13","volume":"30","author":"Y. Yang","year":"2007","unstructured":"Yang, Y., Sun, W.Y.: Adaptive conic trust region method for nonlinear least squares problems. J.\u00a0Nanjing Norm. Univ. 30(1), 13\u201321 (2007)","journal-title":"J.\u00a0Nanjing Norm. Univ."},{"key":"9309_CR26","first-page":"48","volume":"1","author":"Q.M. Han","year":"1995","unstructured":"Han, Q.M., Sheng, S.B.: Conic model algorithms for nonlinear least square problems. Numer. Math. A, J. Chin. Univ. 1, 48\u201359 (1995)","journal-title":"Numer. Math. A, J. Chin. Univ."},{"key":"9309_CR27","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1137\/S036301299223619X","volume":"38","author":"L. Qi","year":"1995","unstructured":"Qi, L., Chen, X.: A globally convergent successive approximation method for nonsmooth equations. SIAM J. Control Optim. 38, 402\u2013418 (1995)","journal-title":"SIAM J. Control Optim."},{"key":"9309_CR28","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1137\/0805011","volume":"5","author":"L. Qi","year":"1995","unstructured":"Qi, L.: Trust region algorithms for solving nonsmooth equation. SIAM J. Optim. 5, 219\u2013230 (1995)","journal-title":"SIAM J. Optim."},{"key":"9309_CR29","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L. Grippo","year":"1986","unstructured":"Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton\u2019s Method. SIAM J. Numer. Anal. 23, 707\u2013716 (1986)","journal-title":"SIAM J. Numer. Anal."},{"key":"9309_CR30","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1016\/S0898-1221(03)00130-5","volume":"45","author":"J.L. Zhang","year":"2003","unstructured":"Zhang, J.L., Zhang, X.S.: A nonmonotone adaptive trust region method and its convergence. Comput. Math. Appl. 45, 1469\u20131477 (2003)","journal-title":"Comput. Math. Appl."},{"key":"9309_CR31","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.amc.2005.01.048","volume":"171","author":"J.T. Mo","year":"2005","unstructured":"Mo, J.T., Zhang, K.C., Wei, Z.X.: A nonmonotone trust region method for unconstrained optimization. Appl. Math. Comput. 171, 371\u2013384 (2005)","journal-title":"Appl. Math. Comput."},{"key":"9309_CR32","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s002450010020","volume":"43","author":"Z.W. Chen","year":"2001","unstructured":"Chen, Z.W., Han, J.Y., Xu, D.C.: A nonmonotone trust region method for nonlinear programming with simple bound constraints. Appl. Math. Optim. 43, 63\u201385 (2001)","journal-title":"Appl. Math. Optim."},{"key":"9309_CR33","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.cam.2007.07.038","volume":"220","author":"S.J. Qu","year":"2008","unstructured":"Qu, S.J., Zhang, K.C., Zhang, J.: A nonmonotone trust region method of conic model for unconstrained optimization. J. Comput. Appl. Math. 220, 119\u2013128 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"9309_CR34","first-page":"493","volume":"76","author":"F. Facchinei","year":"1997","unstructured":"Facchinei, F., Kanzow, C.: A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math. Program. 76, 493\u2013512 (1997)","journal-title":"Math. Program."},{"key":"9309_CR35","unstructured":"Qi, L.: C-differentiability, C-differential operators and generalized Newton methods. Technical Report AMR96\/5, School of Mathematics, The University of New South Wales, Sydney, Australia (1996)"},{"key":"9309_CR36","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1137\/S1052623497328781","volume":"9","author":"C. Kanzow","year":"1999","unstructured":"Kanzow, C., Pieper, H.: Jacobian smoothing methods for nonlinear complementarity problems. SIAM J. Optim. 9, 342\u2013373 (1999)","journal-title":"SIAM J. Optim."},{"key":"9309_CR37","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.camwa.2007.02.003","volume":"54","author":"Y. Ji","year":"2007","unstructured":"Ji, Y., Zhang, K.C., Qu, S.J., Zhou, Y.: A trust region method by active-set strategy for general nonlinear optimization. Comput. Math. Appl. 54, 229\u2013241 (2007)","journal-title":"Comput. Math. Appl."},{"key":"9309_CR38","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1090\/S0025-5718-98-00932-6","volume":"222","author":"X. Chen","year":"1998","unstructured":"Chen, X., Qi, L., Sun, D.: Global and superlinear convergence of the smoothing Newton method and its applications to general box constrained variational inequalities. Math. Comput. 222, 519\u2013540 (1998)","journal-title":"Math. Comput."},{"key":"9309_CR39","unstructured":"Gertz, E.M.: Combination trust-region line search methods for unconstrained optimization. University of California, San Diego (1999)"},{"key":"9309_CR40","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1012903105391","volume":"103","author":"J. Sun","year":"2001","unstructured":"Sun, J., Zhang, J.P.: Global convergence of conjugate gradient methods without line search. Ann. Oper. Res. 103, 161\u2013173 (2001)","journal-title":"Ann. Oper. Res."},{"key":"9309_CR41","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0377-0427(02)00416-8","volume":"146","author":"X.D. Chen","year":"2002","unstructured":"Chen, X.D., Sun, J.: Global convergence of a two-parameter family of conjugate gradient methods without line search. J. Comput. Appl. Math. 146, 37\u201345 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"9309_CR42","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.5.1.43","volume":"5","author":"S.M. Robinson","year":"1980","unstructured":"Robinson, S.M.: Strongly regular generalized equation. Math. Oper. Res. 5, 43\u201362 (1980)","journal-title":"Math. Oper. Res."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9309-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9309-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9309-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:38Z","timestamp":1559302598000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9309-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,1]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["9309"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9309-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,1]]}}}