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dc.contributorVirginia Tech
dc.contributor.authorYuan, Y. B.
dc.contributor.authorFan, W. G.
dc.contributor.authorPu, D. M.
dc.date.accessioned2014-05-14T13:23:41Z
dc.date.available2014-05-14T13:23:41Z
dc.date.issued2007-08
dc.identifier.citationYuan, Y. B.; Fan, W. G.; Pu, D. M., "Spline function smooth support vector machine for classification," J. Industrial and Management Optimization 3(3), 529-542, (2007); DOI: 10.3934/jimo.2007.3.529
dc.identifier.issn1547-5816
dc.identifier.urihttp://hdl.handle.net/10919/47978
dc.description.abstractThis paper presents a duality theory for solving concave minimization problem and nonconvex quadratic programming problem subjected to nonlinear inequality constraints. By use of the canonical dual transformation developed recently, two canonical dual problems are formulated, respectively. These two dual problems are perfectly dual to the primal problems with zero duality gap. It is proved that the sufficient conditions for global minimizers and local extrema (both minima and maxima) are controlled by the triality theory discovered recently [5]. This triality theory can be used to develop certain useful primal-dual methods for solving difficult nonconvex minimization problems. Results shown that the difficult quadratic minimization problem with quadratic constraint can be converted into a one-dimensional dual problem, which can be solved completely to obtain all KKT points and global minimizer.
dc.language.isoen_US
dc.publisherAmerican Institute of Mathematical Sciences
dc.subjectglobal optimization
dc.subjectduality
dc.subjectconcave minimization
dc.subjectquadratic
dc.subjectprogramming
dc.subjectnp-hard problems
dc.subjectoptimality condition
dc.subjectengineering, multidisciplinary
dc.subjectoperations research & management
dc.subjectscience
dc.subjectmathematics, interdisciplinary applications
dc.titleSpline function smooth support vector machine for classification
dc.typeArticle - Refereed
dc.identifier.urlhttp://aimsciences.org/journals/displayArticlesnew.jsp?paperID=2609
dc.date.accessed2014-05-09
dc.title.serialJournal of Industrial and Management Optimization
dc.identifier.doihttps://doi.org/10.3934/jimo.2007.3.529


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