Conic separation of nite sets I. The homogeneous case.

This work addresses the issue of separating two finite sets in R n by means of a suitable revolution cone

[1]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[2]  Kwangsoo Kim,et al.  Data separation via a finite number of discriminant functions: A global optimization approach , 2007, Appl. Math. Comput..

[3]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[4]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[5]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three space , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[6]  Annabella Astorino,et al.  DC models for spherical separation , 2010, J. Glob. Optim..

[7]  Alexander Zien,et al.  Semi-Supervised Classification by Low Density Separation , 2005, AISTATS.

[8]  Annabella Astorino,et al.  Ellipsoidal separation for classification problems , 2005, Optim. Methods Softw..

[9]  Refail Kasimbeyli,et al.  A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization , 2009, SIAM J. Optim..

[10]  Antonio Fuduli,et al.  Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control , 2003, SIAM J. Optim..

[11]  P. H. Quang,et al.  Regularity conditions for constrained extremum problems via image space , 1994 .

[12]  O. Mangasarian.  Linear and Nonlinear Separation of Patterns by Linear Programming , 1965 .

[13]  M. I. Henig.  A cone separation theorem , 1982 .

[14]  Annabella Astorino,et al.  Polyhedral Separability Through Successive LP , 2002 .

[15]  Le Thi Hoai An,et al.  An Efficient DCA for Spherical Separation , 2011, ACIIDS.

[16]  Hiroshi Konno,et al.  Failure Discrimination by Semi-Definite Programming , 2002 .

[17]  James E. Falk,et al.  Robust separation of finite sets via quadratics , 2001, Comput. Oper. Res..

[18]  S. Odewahn,et al.  Automated star/galaxy discrimination with neural networks , 1992 .

[19]  Massimo Pappalardo.  On the Image Regularity Condition , 2004 .

[20]  Le Thi Hoai An,et al.  A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem , 1998, SIAM J. Optim..

[21]  Annabella Astorino,et al.  Conic separation of finite sets II . The non-homogeneous case , 2013 .

[22]  Kristin P. Bennett,et al.  Fast Bundle Algorithm for Multiple-Instance Learning , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Rafail N. Gasimov,et al.  Separation via polyhedral conic functions , 2006, Optim. Methods Softw..