Successive overrelaxation for support vector machines

IEEE Transactions on Neural Networks

Volumn 10, Issue 5, 1999, Pages 1032-1037

  Mangasarian, Olvi L ^a   Musicant, David R ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; VECTORS;

SUCCESSIVE OVERRELAXATION (SOR); SUPPORT VECTOR MACHINES (SVM);

NEURAL NETWORKS;

EID: 0032594961     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.788643     Document Type: Article

References (27)

1. O. L. Mangasarian, "Solution of symmetric linear complementarity problems by iterative methods," J. Optimization Theory Applicat., vol. 22, no. 4, pp. 465-485, Aug. 1977.
2. _, "On the convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem," SIAM J. Optimization, vol. 1, pp. 114-122, 1991.
3. Z.-Q. Luo and P. Tseng, "Error bounds and convergence analysis of feasible descent methods: A general approach," Ann. Operations Res., vol. 46, pp. 157-178, 1993.
4. V. N. Vapnik, The Nature of Statistical Learning Theory. New York: Springer, 1995.
5. V. Cherkassky and F. Mulier, Learning from Data - Concepts, Theory and Methods. New York: Wiley, 1998.
6. J. Platt, "Sequential minimal optimization: A fast algorithm for training support vector machines," in Advances in Kernel Methods - Support Vector Learning, B. Schölkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 1999, pp. 185-208. Available http://www.research.microsoft.com/~jplatt/smo.html.
7. T. Joachims, "Making large-scale support vector machine learning practical," in Advances in Kernel Methods - Support Vector Learning, B. Schölkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: 1999, pp. 169-184.
8. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic, 1970.
9. J. M. Ortega, Numerical Analysis, A Second Course. New York: Academic, 1972.
10. C. W. Cryer, "The solution of a quadratic programming problem using systematic overrelaxation," SIAM J. Contr. Optimization, vol. 9, pp. 385-392, 1971.
11. J.-S. Pang, "More results on the convergence of iterative methods for the symmetric linear complementarity problem," J. Optimization Theory Applicat., vol. 49, pp. 107-134, 1986.
12. O. L. Mangasarian and R. De Leone, "Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems," Ann. Operations Res., vol. 14, pp. 41-59, 1988.
13. W. Li, "Remarks on convergence of matrix splitting algorithm for the symmetric linear complementarity problem," SIAM J. Optimization, vol. 3, pp. 155-163, 1993.
14. R. De Leone and M. A. T. Roth, "Massively parallel solution of quadratic programs via successive overrelaxation," Concurrency: Practice and Experience, vol. 5, pp. 623-634, 1993.
15. S. P. Dirkse and M. C. Ferns, "MCPLIB: A collection of nonlinear mixed complementarity problems," Optimization Methods and Software, vol. 5, pp. 319-345, 1995. Available ftp://ftp.cs.wisc.edu/tech-reports/reports/94/tr1215.ps
16. T.-T. Friess, N. Cristianini, and C. Campbell, "The kernel-adatron algorithm: A fast and simple learning procedure for support vector machines," in Machine Learning Proc. 15th Int. Conf. (ICML '98), J. Shavlik, Ed. San Mateo, CA: Morgan Kaufmann, 1998, pp. 188-196. Available http://svm.first.gmd.de/papers/FriCriCam98.ps.gz
17. T.-T. Friess, "Support vector neural networks: The kernel adatron with bias and soft margin," Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K., Tech. Rep., 1998. Available www.brunner-edv.com/friess/
18. B. E. Boser, I. M. Guyon, and V. N. Vapnik, "A training algorithm for optimal margin classifiers," in Proc. 5th Annu. ACM Wkshp. Comput. Learning Theory, D. Haussler, Ed. Pittsburgh, PA: ACM Press, July 1992, pp. 144-152.
19. V. N. Vapnik, Estimation of Dependences Based on Empirical Data. New York: Springer-Verlag, 1982.
20. O. L. Mangasarian, Nonlinear Programming. New York: McGraw-Hill, 1969, Reprint: SIAM Classic in Applied Mathematics 10, Philadelphia, PA, 1994.
21. O. L. Mangasarian and D. R. Musicant, "Data discrimination via nonlinear generalized support vector machines," Comput. Sci. Dept., Univ. Wisconsin, Madison, Tech. Rep. 99-03, Mar. 1999. Available ftp://ftp.cs.wisc.edu/math-prog/tech-reports/99-03.ps.Z
22. B. T. Polyak, Introduction to Optimization. New York: Optimization Software, Inc., 1987.
23. P. M. Murphy and D. W. Aha, "UCI repository of machine learning databases," Dept. Inform. Comput. Sci., Univ. California, Irvine, Tech. Rep., 1992. Available www.ics.uci.edu/!mlearn/MLRepository.html
24. light," 1998. Available www-ai.informatik.uni-dortmund.de/FORSCHUNG/VERFAHREN/SVM_LIGHT/svm_light. eng.html
25. P. S. Bradley and O. L. Mangasarian, "Massive data discrimination via linear support vector machines," Comput. Sci. Dept., Univ. Wisconsin, Madison, Tech. Rep. 98-05, May 1998. Optimization Methods Software, to be published. Available ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-03.ps.Z
26. C. Chen and O. L. Mangasarian, "Hybrid misclassification minimization," Advances Comput. Math., vol. 5, no. 2, pp. 127-136, 1996. Available ftp://ftp.cs.wisc.edu/math-prog/tech-reports/95-05.ps.Z
27. R. De Leone, O. L. Mangasarian, and T.-H. Shiau, "Multisweep asynchronous parallel successive overrelaxation for the nonsymmetric linear complementarity problem," Ann. Operations Res., vol. 22, pp. 43-54, 1990.