Gradient projection methods for quadratic programs and applications in training support vector machines

References

• Barzilai , J and Borwein , JM . 1988 . Two point step size gradient methods . IMA Journal on Numerical Analysis , 8 : 141 – 148 .
   Web of Science ®Google Scholar
• Birgin , EG , Martìnez , JM and Raydan , M . 2000 . Nonmonotone spectral projected gradient methods on convex sets . SIAM Journal on Optimization , 10 ( 4 ) : 1196 – 1211 .
   Web of Science ®Google Scholar
• Ruggiero , V and Zanni , L . 2000 . Projection-type methods for large convex quadratic programs: theory and computational experience . Journal of Optimization Theory and Applications , 104 ( 2 ) : 281 – 299 .
   Google Scholar
• Ruggiero V Zanni L 2000 Variable projection methods for large convex quadratic programs In: D. Trigiante (Ed.) Recent Trends in Numerical Analysis Advances in the Theory of Computational Mathematics 3, Nova Science Publ.
   Google Scholar
• Grippo , L , Lampariello , F and Lucidi , S . 1986 . A nonmonotone line search technique for newton's method . SIAM Journal of Numerical Analysis , 23 : 707 – 716 .
   Web of Science ®Google Scholar
• Bertsekas DP 1999 Nonlinear Programming Belmont MA Athena Scientific
   Google Scholar
• Galligani E Ruggiero V Zanni L 2000 Projection-type methods for large convex quadratic programs: theory and computational experience Monograph 5 Scientific Research Program ‘Numerical Analysis: Methods and Mathematical Software’, University of Ferrara Ferrara Italy Available at:, http://www.unife.it/AnNum97/monografie.htm>
   Google Scholar
• Galligani E Ruggiero V Zanni L 2003 Variable projection methods for large-scale quadratic optimization in data analysis applications In: P. Daniele, F. Giannessi and A. Maugeri (Eds) Equili-brium Problems and Variational Models Nonconvex Optimization and Its Applications 68 Boston Kluwer Academic Publishers
   Google Scholar
• Grippo , L and Sciandrone , M . 2002 . Nonmonotone globalization techniques for the Barzilai-Borwein gradient method . Computational Optimization and Applications , 23 : 143 – 169 .
   Web of Science ®Google Scholar
• Zanghirati , G and Zanni , L . 2003 . A parallel solver for large quadratic programs in training support vector machines . Parallel Computing , 29 : 535 – 551 .
   Web of Science ®Google Scholar
• Fung G Mangasarian OL 2001 Proximal support vector machines classifiers Data Mining Institute Technical Report 01-02, Computer Sciences Department, University of Wisconsin Madison WI
   Google Scholar
• Burges , CJC . 1998 . A tutorial on support vector machines for pattern recognition . Data Mining and Knowledge Discovery , 2 ( 2 ) : 121 – 167 .
   Web of Science ®Google Scholar
• Cortes , C and Vapnik , VN . 1995 . Support vector network . Machine Learning , 20 : 1 – 25 .
   Web of Science ®Google Scholar
• Cristianini N Shawe-Taylor J 2000 An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods, Cambridge University Press
   Google Scholar
• Vapnik VN 1998 Statistical Learning Theory New York John Wiley and Sons
   Google Scholar
• Ferris , MC and Munson , TS . 2003 . SIAM Journal on Optimization , 13 : 783 – 804 .
   Web of Science ®Google Scholar
• Chang CC Lin CJ 2002 LIBSVM: A library for support vector machines Available at:, <, http://www.csie.ntu.edu.tw/~cjlin/libsvm, >
   Google Scholar
• Flake , GW and Lawrence , S . 2002 . Efficient SVM regression training with SMO . Machine Learning , 46 ( 1 ) : 271 – 290 .
   Web of Science ®Google Scholar
• Platt JC 1998 Fast training of support vector machines using sequential minimal optimization In: B. Schölkopf, C. Burges and A. Smola (Eds) Advances in Kernel Methods—Support Vector Learning Cambridge MA MIT Press
   Google Scholar
• Collobert , R and Benjo , S . 2001 . SVMTorch: Support Vector Machines for large-scale regression problems . Journal of Machine Learning Research , 1 : 143 – 160 .
   Web of Science ®Google Scholar
• Hsu , CW and Lin , CJ . 2002 . A simple decomposition method for support vector machines . Machine Learning , 46 : 291 – 314 .
   Web of Science ®Google Scholar
• Joachims T 1998 Making large-scale SVM learning practical In: B. Schölkopf, C.J.C. Burges and A. Smola (Eds) Advances in Kernel Methods—Support Vector Learning Cambridge MA MIT Press
   Google Scholar
• Osuna E Freund R Girosi F 1997 An improved training algorithm for support vector machines In: J. Principe, L. Giles, N. Morgan and E. Wilson (Eds) Proceedings of the IEEE Workshop on Neural Networks for Signal Processing, IEEE Press
   Google Scholar
• Dai , YH and Liao , LZ . 2002 . R-linear convergence of the Barzilai and Borwein gradient method . IMA Journal of Numerical Analysis , 22 : 1 – 10 .
   Web of Science ®Google Scholar
• Fletcher R 2001 On the Barzilai–Borwein Method, Numerical Analysis Report NA/207
   Google Scholar
• Dai YH 2001 Alternate stepsize gradient method, AMSS-2001-041, Academy of Mathematics and Systems Sciences Chinese Academy of Sciences China
   Google Scholar
• Dai , YH , Yuan , J and Yuan , Y . 2002 . Modified two-point stepsize gradient methods for unconstrained optimization . Computational Optimizations and Applications , 22 : 103 – 109 .
   Web of Science ®Google Scholar
• Friedlander , A , Martínez , JM , Molina , B and Raydan , M . 1999 . Gradient method with retards and generalizations . SIAM Journal on Numerical Analysis , 36 : 275 – 289 .
   Web of Science ®Google Scholar
• Raydan , M and Svaiter , BF . 2002 . Relaxed steepest descent and Cauchy–Barzilai–Borwein method . Computational Optimization and Applications , 21 : 155 – 167 .
   Web of Science ®Google Scholar
• Fisk , C and Nguyen , S . 1980 . Solution algorithms for network equilibrium models with asymmetric user costs . Transportation Science , 16 : 361 – 381 .
   Web of Science ®Google Scholar
• LeCun Y The MNIST database of handwritten digits Available at:, <, http://yann.lecun.com/exdb/mnist, >
   Google Scholar
• Murphy PM Aha DW 1992 UCI repository of machine learning databases Available at: <, http://www.ics.uci.edu/~mlearn/MLRepository.html, >
   Google Scholar
• Pardalos , PM and Kovoor , N . 1990 . An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds . Mathematical Programming , 46 : 321 – 328 .
   Web of Science ®Google Scholar
• Vanderbei RJ 1998 LOQO: an interior point code for quadratic programming Technical Report SOR-94-15 Revised, Princeton University
   Google Scholar
• Smola AJ 1998 pr_LOQO optimizer Available at: <, http://www.kernel-machines.org/code/prloqo.tar.gz, >
   Google Scholar
• Murtagh B Saunders M 1995 MINOS 5.4 User's Guide, System Optimization Laboratory Stanford University
   Google Scholar
• Lin , CJ . 2001 . On the convergence of the decomposition method for support vector machines . IEEE Transactions on Neural Networks , 12 ( 6 ) : 1288 – 1298 .
   PubMedGoogle Scholar
• Lin CJ 2002 Linear convergence of a decomposition method for support vector machines Technical Report, Department of Computer Science and Information Engineering, National Taiwan University
   Google Scholar