{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T13:08:59Z","timestamp":1723208939009},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,12,30]],"date-time":"2008-12-30T00:00:00Z","timestamp":1230595200000},"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":[[2010,11]]},"DOI":"10.1007\/s10589-008-9229-y","type":"journal-article","created":{"date-parts":[[2009,1,5]],"date-time":"2009-01-05T14:38:19Z","timestamp":1231166299000},"page":"501-527","source":"Crossref","is-referenced-by-count":5,"title":["An aggregate deformation homotopy method for\u00a0min-max-min problems with max-min constraints"],"prefix":"10.1007","volume":"47","author":[{"given":"Hui-juan","family":"Xiong","sequence":"first","affiliation":[]},{"given":"Bo","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,12,30]]},"reference":[{"key":"9229_CR1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/978-3-642-61257-2","volume-title":"Numerical Continuation Methods: An Introduction","author":"E.L. Allgower","year":"1990","unstructured":"Allgower, E.L., Georg, K.: In: Numerical Continuation Methods: An Introduction, pp. 9\u201323. Springer, Berlin\/New York (1990)"},{"key":"9229_CR2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1137\/S1052623401392123","volume":"14","author":"L.T. Andr\u00e9","year":"2003","unstructured":"Andr\u00e9, L.T., Andreas, W., Sasan, B., et al.: A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties. SIAM J. Optim. 14, 173\u2013199 (2003)","journal-title":"SIAM J. Optim."},{"key":"9229_CR3","first-page":"265","volume":"112","author":"A. Astorino","year":"2002","unstructured":"Astorino, A., Gaudioso, M.: Polyhedral separability through successive LP. J. Optim. 112, 265\u2013293 (2002)","journal-title":"J. Optim."},{"key":"9229_CR4","unstructured":"Birbil, S., Fang, S.C., Han, J.: Entropic regularization approach for mathematical programs with equilibrium constraints. Technical Report, Industrial Engineering and Operations Research, Carolina, USA (2002)"},{"key":"9229_CR5","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1007\/s101070050109","volume":"86","author":"W.G. Bofill","year":"1999","unstructured":"Bofill, W.G.: Properties of an interior embedding for solving nonlinear optimization problems. Math. Program. 86, 649\u2013659 (1999)","journal-title":"Math. Program."},{"key":"9229_CR6","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1137\/0325059","volume":"25","author":"R.W. Chaney","year":"1987","unstructured":"Chaney, R.W.: Second-order necessary conditions in constrained semismooth optimization. SIAM J. Control Optim. 25, 1072\u20131081 (1987)","journal-title":"SIAM J. Control Optim."},{"key":"9229_CR7","volume-title":"Nondifferentiable Optimization","author":"V.F. Demyanov","year":"1981","unstructured":"Demyanov, V.F., Vasilief, L.V.: Nondifferentiable Optimization. Nauka, Moscow (1981). (In Russian)"},{"key":"9229_CR8","unstructured":"Fang, S.C., Han, J., Huang, Z.H., Birbil, S.: On the finite termination of an entropy function based smoothing newton method for vertical linear complementarity problems. Technical Report, Industrial Engineering and Operations Research, Carolina, USA (2002)"},{"key":"9229_CR9","series-title":"Lecture Notes in Numerical and Applied Analysis","first-page":"9","volume-title":"Advances Notes in Numerical and Applied Analysis","author":"G.C. Feng","year":"1995","unstructured":"Feng, G.C., Yu, B.: Combined homotopy interior point method for nonlinear programming problems. In: Fujita, H., Yamaguti, M. (eds.) Advances Notes in Numerical and Applied Analysis. Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Tokyo. Lecture Notes in Numerical and Applied Analysis, vol. 14, pp. 9\u201316. Springer, Berlin (1995)"},{"key":"9229_CR10","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1016\/S0362-546X(97)00516-6","volume":"32","author":"G.C. Feng","year":"1998","unstructured":"Feng, G.C., Lin, Z.H., Yu, B.: Existence of an interior pathway to a Kraus-Kuhn-Tucker point of a nonlinear programming problem. Nonlinear Anal. 32, 761\u2013768 (1998)","journal-title":"Nonlinear Anal."},{"key":"9229_CR11","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144502414942","volume":"44","author":"A. Forsgren","year":"2002","unstructured":"Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Rev. 44, 525\u2013597 (2002)","journal-title":"SIAM Rev."},{"key":"9229_CR12","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1137\/060650210","volume":"18","author":"A. Forsgren","year":"2007","unstructured":"Forsgren, A., Gill, P.E., Griffin, J.D.: Iterative solution of augmented systems arising in interior method. SIAM J. Optim. 18, 666\u2013690 (2007)","journal-title":"SIAM J. Optim."},{"key":"9229_CR13","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1016\/j.ejor.2004.08.048","volume":"169","author":"J. Guddat","year":"2006","unstructured":"Guddat, J., Vazquez, F.G., Nowack, D., R\u00fcckmann, J.-J.: A modified standard embedding with jumps in nonlinear optimization. Eur. J. Oper. Res. 169, 1185\u20131206 (2006)","journal-title":"Eur. J. Oper. Res."},{"key":"9229_CR14","first-page":"159","volume-title":"Mathematical Programming with Data Perturbation","author":"J. Guddat","year":"1997","unstructured":"Guddat, J., Vazquez, F.G., Nowack, D.: On the role of the Mangasarian-Fromovitz constraint qualification for penalty, exact penalty and Lagrange multiplier methods. In: Fiacco, A.V. (ed.) Mathematical Programming with Data Perturbation, pp. 159\u2013183. Marcel Dekker, New York (1997)"},{"key":"9229_CR15","first-page":"171","volume":"37","author":"H.T. Jongen","year":"1980","unstructured":"Jongen, H.T., Jonker, P., Twilt, F.: On deformation in optimization. Methods Oper. Res. 37, 171\u2013184 (1980)","journal-title":"Methods Oper. Res."},{"key":"9229_CR16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N. Karmarkar","year":"1984","unstructured":"Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica 4, 373\u2013395 (1984)","journal-title":"Combinatorica"},{"key":"9229_CR17","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1137\/S1052623496298534","volume":"8","author":"C. Kirjner-Neto","year":"1998","unstructured":"Kirjner-Neto, C., Polak, E.: On the conversion of optimization problems with max-min constraints to standard optimization problems. SIAM J. Optim. 8, 887\u2013915 (1998)","journal-title":"SIAM J. Optim."},{"key":"9229_CR18","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1007\/BFb0121217","volume":"21","author":"M. Kojima","year":"1984","unstructured":"Kojima, M., Hirabayashi, R.: Continuous deformations of nonlinear programs. Math. Program. Study 21, 150\u2013198 (1984)","journal-title":"Math. Program. Study"},{"key":"9229_CR19","doi-asserted-by":"crossref","unstructured":"Kort, B.W., Bertsekas, D.P.: A new penalty function algorithm for constrained minimization. In: Proceedings of the 1972 IEEE Conference on Decision and Control, New Orleans, Louisiana (1972)","DOI":"10.1109\/CDC.1972.268971"},{"key":"9229_CR20","first-page":"691","volume":"109","author":"S.J. Li","year":"2001","unstructured":"Li, S.J., Yang, X.Q., Teo, K.L.: On the conversion of optimization problems with max-min constraints to standard optimization problems. J. Optim. 109, 691\u2013698 (2001)","journal-title":"J. Optim."},{"key":"9229_CR21","first-page":"1283","volume":"12","author":"X.S. Li","year":"1991","unstructured":"Li, X.S.: An aggregate function method for nonlinear programming. Sci. China (Ser. A) 12, 1283\u20131288 (1991)","journal-title":"Sci. China (Ser. A)"},{"key":"9229_CR22","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1057\/jors.1991.190","volume":"42","author":"X.S. Li","year":"1991","unstructured":"Li, X.S.: An aggregate constraint method for nonlinear programming. J. Oper. Res. Soc. 42, 1003\u20131010 (1991)","journal-title":"J. Oper. Res. Soc."},{"key":"9229_CR23","first-page":"227","volume":"18","author":"X.S. Li","year":"1992","unstructured":"Li, X.S.: An entropy-based aggregate method for minimax optimization. Eng. Optim. 18, 227\u2013285 (1992)","journal-title":"Eng. Optim."},{"key":"9229_CR24","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF01199466","volume":"46","author":"X.S. Li","year":"1997","unstructured":"Li, X.S., Fang, S.C.: On the entropic regularization method for solving min-max problems with applications. Math. Methods Oper. Res. 46, 119\u2013130 (1997)","journal-title":"Math. Methods Oper. Res."},{"key":"9229_CR25","first-page":"3","volume":"8","author":"X.S. Li","year":"2003","unstructured":"Li, X.S., Pan, S.: Solving the finite min-max problem via an exponential penalty method. Comput. Technol. 8, 3\u201315 (2003)","journal-title":"Comput. Technol."},{"key":"9229_CR26","first-page":"209","volume":"80","author":"Z.H. Lin","year":"1996","unstructured":"Lin, Z.H., Li, Y., Yu, B.: A combined homotopy interior method for general nonlinear programming problem. Appl. Math. Comput. 80, 209\u2013224 (1996)","journal-title":"Appl. Math. Comput."},{"key":"9229_CR27","unstructured":"Liu, G.X.: Aggregate homotopy methods for solving sequential max-min Problems, complementarity problems and variational inequalities. Ph.D. thesis, pp. 14\u201342. Department of Mathematics, Jilin University, Jilin, China (2003)"},{"key":"9229_CR28","first-page":"155","volume":"2","author":"G.X. Liu","year":"2003","unstructured":"Liu, G.X., Feng, G.C., Yu, B.: Aggregate homotopy method for sequential max-min problems. J. JiLin Univ. (Sci. edn.) 2, 155\u2013156 (2003)","journal-title":"J. JiLin Univ. (Sci. edn.)"},{"key":"9229_CR29","first-page":"381","volume":"29","author":"Q.H. Liu","year":"2000","unstructured":"Liu, Q.H., Yu, B., Feng, G.C.: An interior point path-following method for nonconvex programming with quasi normal cone condition. Adv. Math. 29, 381\u2013382 (2000)","journal-title":"Adv. Math."},{"key":"9229_CR30","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s10957-007-9343-5","volume":"137","author":"O.L. Mangasarian","year":"2008","unstructured":"Mangasarian, O.L., Wild, E.W.: Multiple instance classification via successive linear programming. J.\u00a0Optim. 137, 555\u2013568 (2008)","journal-title":"J.\u00a0Optim."},{"key":"9229_CR31","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s10898-005-3845-1","volume":"34","author":"O.L. Mangasarian","year":"2006","unstructured":"Mangasarian, O.L., Rosen, J.B., Thompson, M.E.: Nonconvex piecewise-quadratic underestimation for global minimization. J. Glob. Optim. 34, 475\u2013488 (2006)","journal-title":"J. Glob. Optim."},{"key":"9229_CR32","first-page":"40","volume":"3","author":"F.W. Meng","year":"1999","unstructured":"Meng, F.W., Xia, Z.Q., Hao, Y.: Generalized second-order directional derivatives for a class of nondifferentiable functions. Oper. Res. Trans. 3, 40\u201346 (1999)","journal-title":"Oper. Res. Trans."},{"key":"9229_CR33","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1137\/0315061","volume":"15","author":"R. Mifflin","year":"1977","unstructured":"Mifflin, R.: Semismooth and semoconvex functions in constrained optimization. SIAM J. Control Optim. 15, 959\u2013972 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"9229_CR34","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s101070050104","volume":"86","author":"J.M. Peng","year":"1999","unstructured":"Peng, J.M., Lin, Z.: A non-interior continuation method for generalized linear complementarity problems. Math. Program. 86, 533\u2013563 (1999)","journal-title":"Math. Program."},{"key":"9229_CR35","first-page":"421","volume":"119","author":"E. Polak","year":"2003","unstructured":"Polak, E., Royset, J.O.: Algorithms for finite and semi-infinite min-max-min problems using adaptive smoothing techniques. J. Optim. 119, 421\u2013457 (2003)","journal-title":"J. Optim."},{"key":"9229_CR36","first-page":"459","volume":"119","author":"E. Polak","year":"2003","unstructured":"Polak, E., Royset, J.O., Womersley, R.S.: Algorithms with adaptive smoothing for finite minimax problems. J. Optim. 119, 459\u2013484 (2003)","journal-title":"J. Optim."},{"key":"9229_CR37","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1006\/jmaa.1998.6205","volume":"230","author":"H.D. Qi","year":"1999","unstructured":"Qi, H.D., Liao, L.Z., Lin, Z.: Regularized smoothing approximations to vertical nonlinear complementarity problems. Math. Anal. Appl. 230, 261\u2013276 (1999)","journal-title":"Math. Anal. Appl."},{"key":"9229_CR38","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1023\/A:1022921624832","volume":"25","author":"R.T. Rockafellar","year":"2003","unstructured":"Rockafellar, R.T.: A property of piecewise smooth functions. Comput. Optim. Appl. 25, 247\u2013250 (2003)","journal-title":"Comput. Optim. Appl."},{"key":"9229_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S1052623402406777","volume":"14","author":"J.O. Royset","year":"2003","unstructured":"Royset, J.O., Polak, E., Kiureghian, A.D.: Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problems. SIAM J. Optim. 14, 1\u201334 (2003)","journal-title":"SIAM J. Optim."},{"key":"9229_CR40","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1287\/opre.1030.0102","volume":"52","author":"S. Scholtes","year":"2004","unstructured":"Scholtes, S.: Nonconvex structures in nonlinear programming. Oper. Res. 52, 368\u2013383 (2004)","journal-title":"Oper. Res."},{"key":"9229_CR41","unstructured":"Shang, Y.F.: Constraint shifting combined homotopy method for nonlinear programming, equilibrium programming and variational inequalities. Ph.D. thesis, pp. 14\u201352. Department of Mathematics, Jilin University, Jilin, China (2006)"},{"key":"9229_CR42","unstructured":"Sun, W.J.: Study on homotopy methods for a local minimum of nonconvex programming problem, M.S. thesis, JinLin University, China (2006)"},{"key":"9229_CR43","unstructured":"Wang, Y.: The computer implementation of the homotopy method for optimization problems, pp. 44\u201364. Dalian Maritime University Press, China (1996)"},{"key":"9229_CR44","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1137\/S105262349936121X","volume":"11","author":"L.T. Watson","year":"2000","unstructured":"Watson, L.T.: Theory of globally convergent probability-one homotopies for nonlinear programming. SIAM J. Optim. 11, 761\u2013780 (2000)","journal-title":"SIAM J. Optim."},{"key":"9229_CR45","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1145\/29380.214343","volume":"13","author":"L.T. Watson","year":"1987","unstructured":"Watson, L.T., Billups, S.C., Morgan, A.P.: Algorithm 652 hompack a suite of codes for globally convergent homotopy algorithms. ACM Trans. Math. Softw. 13, 281\u2013310 (1987)","journal-title":"ACM Trans. Math. Softw."},{"key":"9229_CR46","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1137\/S1052623497322279","volume":"9","author":"M.H. Wright","year":"1998","unstructured":"Wright, M.H.: Ill-conditioning and computational error in interior methods for nonlinear programming. SIAM J. Optim. 9, 84\u2013111 (1998)","journal-title":"SIAM J. Optim."},{"key":"9229_CR47","first-page":"25","volume":"21","author":"Q. Xu","year":"2005","unstructured":"Xu, Q., Yu, B.: Homotopy method for non-convex programming in unbounded set. Northeast. Math. 21, 25\u201331 (2005)","journal-title":"Northeast. Math."},{"key":"9229_CR48","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1023\/A:1011211101714","volume":"20","author":"S. Xu","year":"2001","unstructured":"Xu, S.: Smoothing method for minimax problems. Comput. Optim. Appl. 20, 267\u2013279 (2001)","journal-title":"Comput. Optim. Appl."},{"key":"9229_CR49","first-page":"81","volume":"23","author":"Q.Z. Yang","year":"2001","unstructured":"Yang, Q.Z., Yang, D.Z., Zhang, M.H.: Adjustable entropy function method. Math. Numer. Sinica 23, 81\u201386 (2001)","journal-title":"Math. Numer. Sinica"},{"key":"9229_CR50","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1137\/S1052623499355533","volume":"14","author":"H. Yamashita","year":"2003","unstructured":"Yamashita, H., Yabe, H.: An interior point method with a primal-dual quadratic barrier penalty function for nonlinear optimization. SIAM J. Optim. 14, 479\u2013499 (2003)","journal-title":"SIAM J. Optim."},{"key":"9229_CR51","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/S0362-546X(99)00420-4","volume":"45","author":"B. Yu","year":"2001","unstructured":"Yu, B., Feng, G.C., Zheng, S.L.: The aggregate constraint homotopy method for nonconvex nonlinear programming. Nonlinear. Anal. 45, 839\u2013847 (2001)","journal-title":"Nonlinear. Anal."},{"key":"9229_CR52","first-page":"287","volume":"19","author":"B. Yu","year":"2003","unstructured":"Yu, B., Liu, G.X., Feng, G.C., Li, Y.: The aggregate homotopy method for constrained sequential max-min problems. Northeast. Math. 19, 287\u2013290 (2003)","journal-title":"Northeast. Math."},{"key":"9229_CR53","first-page":"383","volume":"16","author":"B. Yu","year":"2000","unstructured":"Yu, B., Liu, Q.H., Feng, G.C.: A combined homotopy interior point method for nonconvex programming with pseudo cone condition. Northeast. Math. 16, 383\u2013386 (2000)","journal-title":"Northeast. Math."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9229-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-008-9229-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-008-9229-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T07:36:36Z","timestamp":1559288196000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-008-9229-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,30]]},"references-count":53,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,11]]}},"alternative-id":["9229"],"URL":"https:\/\/doi.org\/10.1007\/s10589-008-9229-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,30]]}}}