{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:49:49Z","timestamp":1778597389790,"version":"3.51.4"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1996,3,1]],"date-time":"1996-03-01T00:00:00Z","timestamp":825638400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Applic"],"published-print":{"date-parts":[[1996,3]]},"DOI":"10.1007\/bf00249052","type":"journal-article","created":{"date-parts":[[2004,9,26]],"date-time":"2004-09-26T15:12:28Z","timestamp":1096211548000},"page":"97-138","source":"Crossref","is-referenced-by-count":386,"title":["A class of smoothing functions for nonlinear and mixed complementarity problems"],"prefix":"10.1007","volume":"5","author":[{"given":"Chunhui","family":"Chen","sequence":"first","affiliation":[]},{"given":"O. L.","family":"Mangasarian","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF00249052_CR1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1137\/0320018","volume":"20","author":"D.P. Bertsekas","year":"1982","unstructured":"D.P. Bertsekas, \u201cProjected Newton methods for optimization problems with simple constraints\u201d, SIAM Journal on Control and Optimization, vol. 20, pp. 221\u2013246, 1982.","journal-title":"SIAM Journal on Control and Optimization"},{"key":"BF00249052_CR2","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1137\/0614081","volume":"14","author":"B. Chen","year":"1993","unstructured":"B. Chen and P.T. Harker, \u201cA non-interior-point continuation method for linear complementarity problems\u201d, SIAM Journal on Matrix Analysis and Applications, vol. 14, pp. 1168\u20131190, 1993.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"BF00249052_CR3","series-title":"Technical Report","volume-title":"Smoothing methods for convex inequalities and linear complementarity problems","author":"C. Chen","year":"1993","unstructured":"C. Chen and O.L. Mangasarian, \u201cSmoothing methods for convex inequalities and linear complementarity problems\u201d, Technical Report 1191, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 53706, November 1993. (To appear in Mathematical Programming, vol. 71, 1995.)"},{"key":"BF00249052_CR4","volume-title":"Variational Inequalities and Complementarity Problems","author":"R.W. Cottle","year":"1980","unstructured":"R.W. Cottle, F. Giannessi, and J.-L. Lions, Variational Inequalities and Complementarity Problems, John Wiley & Sons: New York, 1980."},{"key":"BF00249052_CR5","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"J.E. Dennis","year":"1983","unstructured":"J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall: Englewood Cliffs, N.J., 1983."},{"key":"BF00249052_CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1080\/10556789508805606","volume":"5","author":"S.P. Dirkse","year":"1995","unstructured":"S.P. Dirkse and M.C. Ferris, \u201cThe path solver: A non-monotone stabilization scheme for mixed complementarity problems\u201d, Optimization Methods and Software, vol. 5, pp. 123\u2013156, 1995.","journal-title":"Optimization Methods and Software"},{"key":"BF00249052_CR7","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/10556789508805619","volume":"5","author":"S.P. Dirkse","year":"1995","unstructured":"S.P. Dirkse and M.C. Ferris, \u201cMCPLIB: A collection of nonlinear mixed complementarity problems\u201d, Optimization Methods and Software, vol. 5, pp. 319\u2013345, 1995.","journal-title":"Optimization Methods and Software"},{"key":"BF00249052_CR8","unstructured":"S.P. Dirkse, M.C. Ferris, P.V. Preckel, and T. Rutherford, \u201cThe GAMS callable program library for variational and complementarity solvers\u201d, Manuscript, University of Wisconsin, 1993."},{"key":"BF00249052_CR9","series-title":"Technical Report","volume-title":"On the extended linear complementarity problem","author":"M.S. Gowda","year":"1994","unstructured":"M.S. Gowda, \u201cOn the extended linear complementarity problem\u201d, Technical Report, Department of Mathematics & Statistics, University of Maryland Baltimore Country, Baltimore, Maryland, 1994, Mathematical Programming, to appear."},{"key":"BF00249052_CR10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01582255","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and J.-S. Pang, \u201cFinite-dimensional variational inequality and nonlinear complementarty problems: A survey of theory, algorithms and applications\u201d, Mathematical Programming, vol. 48, pp. 161\u2013220, 1990.","journal-title":"Mathematical Programming"},{"key":"BF00249052_CR11","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF01582262","volume":"48","author":"P.T. Harker","year":"1990","unstructured":"P.T. Harker and B. Xiao, \u201cNewton's method for the nonlinear complementarity problem: A B-differentiable equation approach\u201d, Mathematical Programming, vol. 48, pp. 339\u2013357, 1990.","journal-title":"Mathematical Programming"},{"key":"BF00249052_CR12","doi-asserted-by":"crossref","DOI":"10.1063\/1.2810360","volume-title":"Introduction to the Theory of Neural Computation","author":"J. Hertz","year":"1991","unstructured":"J. Hertz, A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley: Redwood City, California, 1991."},{"key":"BF00249052_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms I","author":"J.-B. Hiriart-Urruty","year":"1993","unstructured":"J.-B. Hiriart-Urruty and C. Lemar\u00e9chal, Convex Analysis and Minimization Algorithms I, Springer-Verlag: Berlin, 1993."},{"key":"BF00249052_CR14","series-title":"Technical Summary Report","volume-title":"Newton's method for generalized equations","author":"N.H. Josephy","year":"1979","unstructured":"N.H. Josephy, \u201cNewton's method for generalized equations\u201d, Technical Summary Report 1965, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, 1979."},{"key":"BF00249052_CR15","volume-title":"Some tools allowing interior-point methods to become noninterior","author":"C. Kanzow","year":"1994","unstructured":"C. Kanzow, \u201cSome tools allowing interior-point methods to become noninterior\u201d, Technical Report, Institute of Applied Mathematics, University of Hamburg, Germany, 1994."},{"key":"BF00249052_CR16","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0024-3795(91)90271-W","volume":"152","author":"M. Kojima","year":"1991","unstructured":"M. Kojima and N. Megiddo, \u201cThe relation between the path of centers and smale's regularization of the linear programming problem\u201d, Linear Algebra and Its Applications, vol. 152, pp. 135\u2013139, 1991.","journal-title":"Linear Algebra and Its Applications"},{"key":"BF00249052_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01587074","volume":"44","author":"M. Kojima","year":"1989","unstructured":"M. Kojima, S. Mizuno, and A. Yoshise, \u201cA polynomial-time algorithms for a class of linear complementarity problems\u201d, Mathematical Programming, vol. 44, pp. 1\u201327, 1989.","journal-title":"Mathematical Programming"},{"key":"BF00249052_CR18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF02060937","volume":"39","author":"J. Kreimer","year":"1992","unstructured":"J. Kreimer and R.Y. Rubinstein, \u201cNondifferentiable optimization via smooth approximation: General analytical approach\u201d, Annals of Operations Research, vol. 39, pp. 97\u2013119, 1992.","journal-title":"Annals of Operations Research"},{"issue":"no. 2","key":"BF00249052_CR19","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1137\/0803010","volume":"3","author":"K. Madsen","year":"1993","unstructured":"K. Madsen and H.B. Nielsen, \u201cA finite smoothing algorithm for linear l 1 estimation\u201d, SIAM on Optimization, vol. 3, no. 2, pp. 223\u2013235, May 1993.","journal-title":"SIAM on Optimization"},{"issue":"no. 4","key":"BF00249052_CR20","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1287\/ijoc.5.4.349","volume":"5","author":"O.L. Mangasarian","year":"1993","unstructured":"O.L. Mangasarian, \u201cMathematical programming in neural networks\u201d, ORSA Journal on Computing, vol. 5, no. 4, pp. 349\u2013360, 1993.","journal-title":"ORSA Journal on Computing"},{"key":"BF00249052_CR21","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 problems\u201d, SIAM Journal on Matrix Analysis and Applications, vol. 16, pp. 359\u2013368, 1995.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"BF00249052_CR22","series-title":"Technical Report Preprint MCS-P429-0494","doi-asserted-by":"crossref","DOI":"10.2172\/204261","volume-title":"Global methods for nonlinear complementarity problems","author":"Jorge J. Mor\u00e9","year":"1994","unstructured":"Jorge J. Mor\u00e9, \u201cGlobal methods for nonlinear complementarity problems\u201d, Technical Report Preprint MCS-P429\u20130494, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, 1994."},{"key":"BF00249052_CR23","doi-asserted-by":"crossref","unstructured":"B.A. Murtagh and M.A. Saunders, \u201cMINOS 5.0 user's guide\u201d, Technical Report SOL 83.20, Stanford University, December 1983.","DOI":"10.21236\/ADA138522"},{"key":"BF00249052_CR24","volume-title":"Linear Complementarity, Linear and Nonlinear Programming","author":"K.G. Murty","year":"1988","unstructured":"K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Helderman-Verlag: Berlin, 1988."},{"key":"BF00249052_CR25","unstructured":"J.M. Ortega, Numerical Analysis, A Second Course, Academic Press, 1972."},{"key":"BF00249052_CR26","first-page":"331","volume":"15","author":"J.-S. Pang","year":"1990","unstructured":"J.-S. Pang, \u201cNewton's method for B-differentiable equations\u201d, Mathematics of Operations Research, vol. 15, pp. 331\u2013341, 1990.","journal-title":"Mathematics of Operations Research"},{"key":"BF00249052_CR27","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF01586928","volume":"51","author":"J.-S. Pang","year":"1991","unstructured":"J.-S. Pang, \u201cA B-differentiable equation based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems\u201d, Mathematical Programming, vol. 51, pp. 101\u2013131, 1991.","journal-title":"Mathematical Programming"},{"key":"BF00249052_CR28","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01580617","volume":"60","author":"J.-S. Pang","year":"1993","unstructured":"J.-S. Pang and S.A. Gabriel, \u201cNE\/SQP: A robust algorthm for the nonlinear complementarity problem\u201d, Mathematical Programming, vol. 60, pp. 295\u2013337, 1993.","journal-title":"Mathematical Programming"},{"key":"BF00249052_CR29","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1137\/0804027","volume":"4","author":"M.C. Pinar","year":"1994","unstructured":"M.C. Pinar and S.A. Zenios \u201cOn smoothing exact penalty functions for convex constrained optimization\u201d, SIAM Journal on Optimization, vol. 4, pp. 486\u2013511, 1994.","journal-title":"SIAM Journal on Optimization"},{"key":"BF00249052_CR30","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1287\/moor.19.2.352","volume":"19","author":"D. Ralph","year":"1994","unstructured":"D. Ralph, \u201cGlobal convergence of damped Newton's method for nonsmooth equations via the path search\u201d, Mathematics of Operations Research, vol. 19, pp. 352\u2013389, 1994.","journal-title":"Mathematics of Operations Research"},{"key":"BF00249052_CR31","series-title":"Technical Report","volume-title":"Computable error bounds in mathematical programming","author":"J. Ren","year":"1993","unstructured":"J. Ren, \u201cComputable error bounds in mathematical programming\u201d, Technical Report 1173, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin 53706, August 1993."},{"key":"BF00249052_CR32","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/BFb0120850","volume":"10","author":"S.M. Robinson","year":"1979","unstructured":"S.M. Robinson, \u201cGeneralized equations and their solution: Part I: Basic theory\u201d, Mathematical Programming Study, vol. 10, pp. 128\u2013140, 1979.","journal-title":"Mathematical Programming Study"},{"key":"BF00249052_CR33","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.5.1.43","volume":"5","author":"S.M. Robinson","year":"1980","unstructured":"S.M. Robinson, \u201cStrongly regular generalized equations\u201d, Mathematics of Operations Research, vol. 5, pp. 43\u201362, 1980.","journal-title":"Mathematics of Operations Research"},{"key":"BF00249052_CR34","volume-title":"Newton's method for a class of nonsmooth functions","author":"S.M. Robinson","year":"1988","unstructured":"S.M. Robinson, \u201cNewton's method for a class of nonsmooth functions\u201d, Working Paper, Department of Industrial Engineering, University of Wisconsin, Madison, Wisconsin, 1988."},{"key":"BF00249052_CR35","volume-title":"MILES: A mixed inequality and nonlinear equation solver","author":"T.F. Rutherford","year":"1993","unstructured":"T.F. Rutherford, \u201cMILES: A mixed inequality and nonlinear equation solver\u201d, Working Paper, Department of Economics, University of Colorado, Boulder, 1993."},{"key":"BF00249052_CR36","first-page":"172","volume-title":"Proceedings of the International Congress of Mathematicians","author":"S. Smale","year":"1987","unstructured":"S. Smale, \u201cAlgorithms for solving equations\u201d, In Proceedings of the International Congress of Mathematicians, pp. 172\u2013195, Ameri. Math. Soc., Providence, 1987."},{"key":"BF00249052_CR37","unstructured":"B. Xiao, \u201cGlobal Newtons methods for nonlinear programs and variational inequalities\u201d, Technical Report, Ph.D. Thesis, Department of Decision Sciences, The Wharton School, University of Pennsylvania, Philadelphia, PA, 1990."},{"key":"BF00249052_CR38","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\u201d, Mathematics of Operations Research, vol. 18, pp. 334\u2013345, 1993.","journal-title":"Mathematics of Operations Research"},{"key":"BF00249052_CR39","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BF01581628","volume":"19","author":"I. Zang","year":"1980","unstructured":"I. Zang, \u201cA smoothing-out technique for min-max optimization\u201d, Mathematical Programming, vol. 19, pp. 61\u201377, 1980.","journal-title":"Mathematical Programming"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00249052.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF00249052\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00249052","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T15:56:01Z","timestamp":1554306961000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF00249052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["BF00249052"],"URL":"https:\/\/doi.org\/10.1007\/bf00249052","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}