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Volumn 21, Issue 1, 2011, Pages 361-390

An affine-scaling interior-point method for continuous knapsack constraints with application to support vector machines

Author keywords

Affine scaling; Cyclic Barzilai Borwein methods; Global convergence; Interior point; Linear convergence; Support vector machines

Indexed keywords

AFFINE-SCALING; CYCLIC BARZILAI-BORWEIN METHODS; GLOBAL CONVERGENCE; INTERIOR-POINT; LINEAR CONVERGENCE;

EID: 79957510063     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090766255     Document Type: Article
Times cited : (20)

References (68)
  • 1
    • 84966275544 scopus 로고
    • Minimization of functions having Lipschitz continuous first partial derivatives
    • L. ARMIJO, Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J. Math., 16 (1966), pp. 1-3.
    • (1966) Pacific J. Math. , vol.16 , pp. 1-3
    • Armijo, L.1
  • 3
    • 0001531895 scopus 로고
    • Two point step size gradient methods
    • J. BARZILAI AND J. M. BORWEIN, Two point step size gradient methods, IMA J. Numer. Anal., 8 (1988), pp. 141-148.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 141-148
    • Barzilai, J.1    Borwein, J.M.2
  • 4
    • 0036794059 scopus 로고    scopus 로고
    • Large-scale active-set box-constrained optimization method with spectral projected gradients
    • DOI 10.1023/A:1019928808826
    • E. G. BIRGIN AND J. M. MARTÍNEZ, Large-scale active-set box-constrained optimization method with spectral projected gradients, Comput. Optim. Appl., 23 (2002), pp. 101-125. (Pubitemid 35167001)
    • (2002) Computational Optimization and Applications , vol.23 , Issue.1 , pp. 101-125
    • Birgin, E.G.1    Mario Martinez, J.2
  • 5
    • 0034345420 scopus 로고    scopus 로고
    • Nonmonotone spectral projected gradient methods for convex sets
    • E. G. BIRGIN, J. M. MARTÍNEZ, AND M. RAYDAN, Nonmonotone spectral projected gradient methods for convex sets, SIAM J. Optim., 10 (2000), pp. 1196-1211.
    • (2000) SIAM J. Optim. , vol.10 , pp. 1196-1211
    • Birgin, E.G.1    Martínez, J.M.2    Raydan, M.3
  • 6
    • 18044400238 scopus 로고    scopus 로고
    • Algorithm 813: SPG - Software for Convex-Constrained Optimization
    • DOI 10.1145/502800.502803
    • E. G. BIRGIN, J. M. MARTÍNEZ, AND M. RAYDAN, Algorithm 813: SPG-software for convexconstrained optimization, ACM Trans. Math. Software, 27 (2001), pp. 340-349. (Pubitemid 33654982)
    • (2001) ACM Transactions on Mathematical Software , vol.27 , Issue.3 , pp. 340-349
    • Birgin, E.G.1    Martinez, J.M.2    Raydan, M.3
  • 7
    • 0142199775 scopus 로고    scopus 로고
    • Inexact spectral projected gradient methods on convex sets
    • DOI 10.1093/imanum/23.4.539
    • E. G. BIRGIN, J. M. MARTÍNEZ, AND M. RAYDAN, Inexact spectral projected gradient methods on convex sets, IMA J. Numer. Anal., 23 (2003), pp. 539-559. (Pubitemid 37445929)
    • (2003) IMA Journal of Numerical Analysis , vol.23 , Issue.4 , pp. 539-559
    • Birgin, E.G.1    Martinez, J.M.2    Raydan, M.3
  • 8
    • 84902205493 scopus 로고    scopus 로고
    • Comparison of View-Based Object Recognition Algorithms Using Realistic 3D Models
    • Artificial Neural Networks - ICANN 96
    • V. BLANZ, B. SCHÖLKOPF, H. BÜLTHOFFAND, C. BURGES, V. N. VAPNIK, AND T. VETTER, Comparison of view-based object recognition algorithms using realistic 3d models, in Artificial Neural Networks, ICIANN '96, Lecture Notes in Comput. Sci. 1112 J. V. C. von der Malsburg, W. von Seelen, and B. Sendhoff, eds., Springer, Berlin, 1996, pp. 251-256. (Pubitemid 126098540)
    • (1996) LECTURE NOTES IN COMPUTER SCIENCE , Issue.1112 , pp. 251-256
    • Blanz, V.1    Schoelkopf, B.2    Buelthoff, H.3    Burges, C.4    Vapnik, V.5    Vetter, T.6
  • 11
    • 27144489164 scopus 로고    scopus 로고
    • A tutorial on support vector machines for pattern recognition
    • C. BURGES, A tutorial on support vector machines for pattern recognition, Data Min. Knowl. Disc., 2 (1998), pp. 121-167. (Pubitemid 128695475)
    • (1998) Data Mining and Knowledge Discovery , vol.2 , Issue.2 , pp. 121-167
    • Burges, C.J.C.1
  • 12
    • 84898957872 scopus 로고    scopus 로고
    • Improving the accuracy and speed of support vector machines
    • M. Mozer, M. Jordan, and T. Petsche, eds., MIT Press, Cambridge, MA
    • C. BURGES AND B. SCHÖLKOPF, Improving the accuracy and speed of support vector machines, in Advances in Neural Information Processing Systems 9 M. Mozer, M. Jordan, and T. Petsche, eds., MIT Press, Cambridge, MA, 1997.
    • (1997) Advances in Neural. Information Processing Systems , vol.9
    • Burges, C.1    Schölkopf, B.2
  • 13
    • 0034228643 scopus 로고    scopus 로고
    • The analysis of decomposition methods for support vector machines
    • C.-C. CHANG, C.-W. HSU, AND C.-J. LIN, The analysis of decomposition methods for support vector machines, IEEE Trans. Neural Networks, 11 (2000), pp. 1003-1008.
    • (2000) IEEE Trans. Neural. Networks , vol.11 , pp. 1003-1008
    • Chang, C.-C.1    Hsu, C.-W.2    Lin, C.-J.3
  • 15
    • 34249753618 scopus 로고
    • Support vector networks
    • C. CORTES AND V. VAPNIK, Support vector networks, Mach. Learn., 20 (1995), pp. 1-25.
    • (1995) Mach. Learn. , vol.20 , pp. 1-25
    • Cortes, C.1    Vapnik, V.2
  • 16
    • 0344550334 scopus 로고    scopus 로고
    • Alternate stepsize gradient method
    • Y. H. DAI, Alternate stepsize gradient method, Optimization, 52 (2003), pp. 395-415.
    • (2003) Optimization , vol.52 , pp. 395-415
    • Dai, Y.H.1
  • 17
    • 33644511085 scopus 로고    scopus 로고
    • New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds
    • Y. H. DAI AND R. FLETCHER, New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds, Math. Program., 106 (2006), pp. 403-421.
    • (2006) Math. Program. , vol.106 , pp. 403-421
    • Dai, Y.H.1    Fletcher, R.2
  • 18
    • 33745923778 scopus 로고    scopus 로고
    • The cyclic Barzilai-Borwein method for unconstrained optimization
    • DOI 10.1093/imanum/drl006
    • Y. H. DAI, W. W. HAGER, K. SCHITTKOWSKI, AND H. ZHANG, The cyclic Barzilai-Borwein method for unconstrained optimization, IMA J. Numer. Anal., 26 (2006), pp. 604-627. (Pubitemid 44048227)
    • (2006) IMA Journal of Numerical Analysis , vol.26 , Issue.3 , pp. 604-627
    • Dai, Y.-H.1    Hager, W.W.2    Schittkowski, K.3    Zhang, H.4
  • 19
    • 0035566509 scopus 로고    scopus 로고
    • Adaptive two-point stepsize gradient algorithm
    • DOI 10.1023/A:1013844413130
    • Y. H. DAI AND H. ZHANG, An adaptive two-point stepsize gradient algorithm, Numer. Algorithms, 27 (2001), pp. 377-385. (Pubitemid 33643870)
    • (2001) Numerical Algorithms , vol.27 , Issue.4 , pp. 377-385
    • Dai, Y.-H.1    Zhang, H.2
  • 20
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • DOI 10.1007/s101070100263
    • E. D. DOLAN AND J. J. MORÉ, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), pp. 201-213. (Pubitemid 44744777)
    • (2002) Mathematical Programming, Series B , vol.91 , Issue.2 , pp. 201-213
    • Dolan, E.D.1    More, J.J.2
  • 23
    • 29144499905 scopus 로고    scopus 로고
    • Working set selection using second order information for training support vector machines
    • R.-E. FAN, P.-H. CHEN, AND C.-J. LIN, Working set selection using second order information for training support vector machines, J. Mach. Learn. Res., 6 (2005), pp. 1889-1918. (Pubitemid 41798130)
    • (2005) Journal of Machine Learning Research , vol.6 , pp. 1889-1918
    • Fan, R.-E.1    Chen, P.-H.2    Lin, C.-J.3
  • 24
    • 0041657519 scopus 로고    scopus 로고
    • Interior-point methods for massive support vector machines
    • DOI 10.1137/S1052623400374379, PII S1052623400374379
    • M. C. FERRIS AND T. S. MUNSON, Interior point methods for massive support vector machines, SIAM J. Optim., 13 (2003), pp. 783-804. (Pubitemid 36971112)
    • (2003) SIAM Journal on Optimization , vol.13 , Issue.3 , pp. 783-804
    • Ferris, M.C.1    Munson, T.S.2
  • 25
    • 23944458072 scopus 로고    scopus 로고
    • Semismooth support vector machines
    • DOI 10.1007/s10107-004-0541-8
    • M. C. FERRIS AND T. S. MUNSON, Semismooth support vector machines, Math. Program., 101 (2004), pp. 185-204. (Pubitemid 41201323)
    • (2004) Mathematical Programming , vol.101 , Issue.1 , pp. 185-204
    • Ferris, M.C.1    Munson, T.S.2
  • 26
    • 0041494125 scopus 로고    scopus 로고
    • Efficient SVM training using low-rank kernel representations
    • S. FINE AND K. SCHEINBERG, Efficient SVM training using low-rank kernel representations, J. Mach. Learn. Res., 2 (2001), pp. 243-264.
    • (2001) J. Mach. Learn. Res. , vol.2 , pp. 243-264
    • Fine, S.1    Scheinberg, K.2
  • 28
    • 78650037664 scopus 로고    scopus 로고
    • Using an iterative linear solver in an interior-point method for generating support vector machines
    • DOI 10.1007/s10589-008-9228-z
    • E. M. GERTZ AND J. D. GRIFFIN, Using an iterative linear solver in an interior-point method for generating support vector machines, Comput. Optim. Appl., (2008), DOI 10.1007/s10589-008-9228-z.
    • (2008) Comput. Optim. Appl.
    • Gertz, E.M.1    Griffin, J.D.2
  • 33
    • 0001101633 scopus 로고    scopus 로고
    • Graph partitioning and continuous quadratic programming
    • PII S0895480199335829
    • W. W. HAGER AND Y. KRYLYUK, Graph partitioning and continuous quadratic programming, SIAM J. Discrete Math., 12 (1999), pp. 500-523. (Pubitemid 129643179)
    • (1999) SIAM Journal on Discrete Mathematics , vol.12 , Issue.4 , pp. 500-523
    • Hager, W.W.1    Krylyuk, Y.2
  • 34
    • 60449102102 scopus 로고    scopus 로고
    • An affine-scaling interior-point CBB method for box-constrained optimization
    • W. W. HAGER, B. A. MAIR, AND H. ZHANG, An affine-scaling interior-point CBB method for box-constrained optimization, Math. Program., 119 (2009), pp. 1-32.
    • (2009) Math. Program. , vol.119 , pp. 1-32
    • Hager, W.W.1    Mair, B.A.2    Zhang, H.3
  • 35
    • 33144465578 scopus 로고    scopus 로고
    • A new conjugate gradient method with guaranteed descent and an efficient line search
    • W. W. HAGER AND H. ZHANG, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16 (2005), pp. 170-192.
    • (2005) SIAM J. Optim. , vol.16 , pp. 170-192
    • Hager, W.W.1    Zhang, H.2
  • 36
    • 34249008073 scopus 로고    scopus 로고
    • A new active set algorithm for box constrained optimization
    • DOI 10.1137/050635225
    • W. W. HAGER AND H. ZHANG, A new active set algorithm for box constrained optimization, SIAM J. Optim., 17 (2006), pp. 526-557. (Pubitemid 46798079)
    • (2006) SIAM Journal on Optimization , vol.17 , Issue.2 , pp. 526-557
    • Hager, W.W.1    Zhang, H.2
  • 37
    • 33646392997 scopus 로고    scopus 로고
    • QP algorithms with guaranteed accuracy and run time for support vector machines
    • D. HUSH, P. KELLY, C. SCOVEL, AND I. STEINWART, QP algorithms with guaranteed accuracy and run time for support vector machines, J. Mach. Learn. Res., 7 (2006), pp. 733-769.
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 733-769
    • Hush, D.1    Kelly, P.2    Scovel, C.3    Steinwart, I.4
  • 38
    • 0003425660 scopus 로고    scopus 로고
    • Text categorization with support vector machine
    • University of Dortmund
    • J. JOACHIMS, Text Categorization with Support Vector Machine, Technical report LS VIII Number 23, ftp://ftp-ai.informatik.uni-dortmund.de/pub/Reports/ report23.ps. Z, University of Dortmund, 1997.
    • (1997) Technical Report LS VIII Number 23
    • Joachims, J.1
  • 39
    • 0002714543 scopus 로고    scopus 로고
    • Making large-scale support vector machine learning practical
    • B. Schölkopf, C. Burges, and A. Smola, eds., MIT Press, Cambridge, MA
    • T. JOACHIMS, Making large-scale support vector machine learning practical, in Advances in Kernel Methods-Support Vector Learning, B. Schölkopf, C. Burges, and A. Smola, eds., MIT Press, Cambridge, MA, 1998, pp. 169-184.
    • (1998) Advances in Kernel Methods-support Vector Learning , pp. 169-184
    • Joachims, T.1
  • 42
    • 0036163654 scopus 로고    scopus 로고
    • Convergence of a generalized SMO algorithm for SVM classifier design
    • DOI 10.1023/A:1012431217818
    • S. S. KEERTHI AND E. G. GILBERT, Convergence of a generalized SMO algorithm for SVM classifier design, Mach. Learn., 46 (2002), pp. 351-360. (Pubitemid 34129975)
    • (2002) Machine Learning , vol.46 , Issue.1-3 , pp. 351-360
    • Keerthi, S.S.1    Gilbert, E.G.2
  • 43
    • 0037313407 scopus 로고    scopus 로고
    • SMO algorithm for least-squares SVM formulations
    • DOI 10.1162/089976603762553013
    • S. S. KEERTHI AND S. K. SHEVADE, SMO algorithm for least-squares SVM formulations, Neural Comput., 15 (2003), pp. 487-507. (Pubitemid 37049831)
    • (2003) Neural Computation , vol.15 , Issue.2 , pp. 487-507
    • Keerthi, S.S.1    Shevade, S.K.2
  • 45
    • 0035506741 scopus 로고    scopus 로고
    • On the convergence of the decomposition method for support vector machines
    • DOI 10.1109/72.963765, PII S1045922701064566
    • C.-J. LIN, On the convergence of a decomposition method for support vector machines, IEEE Trans. Neural Networks, 12 (2001), pp. 1288-1298. (Pubitemid 33106034)
    • (2001) IEEE Transactions on Neural Networks , vol.12 , Issue.6 , pp. 1288-1298
    • Lin, C.-J.1
  • 46
    • 0036129250 scopus 로고    scopus 로고
    • Asymptotic convergence of an SMO algorithm without any assumptions
    • DOI 10.1109/72.977319, PII S1045922702009438
    • C.-J. LIN, Asymptotic convergence of an SMO algorithm without any assumptions, IEEE Trans. Neural Networks, 13 (2002), pp. 248-250. (Pubitemid 34236853)
    • (2002) IEEE Transactions on Neural Networks , vol.13 , Issue.1 , pp. 248-250
    • Lin, C.-J.1
  • 48
    • 0000230999 scopus 로고
    • Maxima for graphs and a new proof of a theorem of Turan
    • T. S. MOTZKIN AND E. G. STRAUSS, Maxima for graphs and a new proof of a theorem of Turan, Canad. J. Math., 17 (1965), pp. 533-540.
    • (1965) Canad. J. Math. , vol.17 , pp. 533-540
    • Motzkin, T.S.1    Strauss, E.G.2
  • 50
    • 0003425662 scopus 로고    scopus 로고
    • Support vector machines: Training and applications
    • C. B. C. L. Paper No. 144, MIT, Cambridge, MA
    • E. OSUNA, R. FREUND, AND F. GIROSI, Support Vector Machines: Training and Applications, Technical report AIM-1602, C. B. C. L. Paper No. 144, MIT, Cambridge, MA, 1997.
    • (1997) Technical Report AIM-1602
    • Osuna, E.1    Freund, R.2    Girosi, F.3
  • 53
    • 0003120218 scopus 로고    scopus 로고
    • Fast training of support vector machines using sequential minimal optimization
    • B. Schölkopf, C. Burges, and A. Smola, eds., MIT Press, Cambridge, MA
    • J. PLATT, Fast training of support vector machines using sequential minimal optimization, in Advances in Kernel Methods-Support Vector Learning, B. Schölkopf, C. Burges, and A. Smola, eds., MIT Press, Cambridge, MA, 1998, pp. 41-65.
    • (1998) Advances in Kernel Methods-support Vector Learning , pp. 41-65
    • Platt, J.1
  • 54
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • M. RAYDAN, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem, SIAM J. Optim., 7 (1997), pp. 26-33.
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 55
    • 0036471006 scopus 로고    scopus 로고
    • Relaxed steepest descent and Cauchy-Barzilai-Borwein method
    • DOI 10.1023/A:1013708715892
    • M. RAYDAN AND B. F. SVAITER, Relaxed steepest descent and Cauchy-Barzilai-Borwein method, Comput. Optim. Appl., 21 (2002), pp. 155-167. (Pubitemid 34168103)
    • (2002) Computational Optimization and Applications , vol.21 , Issue.2 , pp. 155-167
    • Raydan, M.1    Svaiter, B.F.2
  • 56
    • 33745798002 scopus 로고    scopus 로고
    • An efficient implementation of an active set method for SVMs
    • K. SCHEINBERG, An efficient implementation of an active set method for SVMs, J. Mach. Learn. Res., 7 (2006), pp. 2237-2257. (Pubitemid 44611764)
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 2237-2257
    • Scheinberg, K.1
  • 59
    • 84902142380 scopus 로고    scopus 로고
    • Incorporating Invariances in Support Vector Learning Machines
    • Artificial Neural Networks - ICANN 96
    • B. SCHÖLKOPF, Incorporating invariances in support vector learning machines, in Artificial Neural Networks, J. V. C. von der Malsburg, W. von Seelen, and B. Sendhoff, eds., Springer, Berlin, 1996, pp. 47-52. (Pubitemid 126098507)
    • (1996) LECTURE NOTES IN COMPUTER SCIENCE , Issue.1112 , pp. 47-52
    • Schoelkopf, B.1    Burges, C.2    Vapnik, V.3
  • 60
    • 12444278992 scopus 로고    scopus 로고
    • Gradient projection methods for quadratic programs and applications in training support vector machines
    • T. SERAFINI, G. ZANGHIRATI, AND L. ZANNI, Gradient projection methods for quadratic programs and applications in training support vector machines, Optim. Methods Softw., 20 (2005), pp. 353-378.
    • (2005) Optim. Methods Softw. , vol.20 , pp. 353-378
    • Serafini, T.1    Zanghirati, G.2    Zanni, L.3
  • 61
    • 27744479938 scopus 로고    scopus 로고
    • On the working set selection in gradient projection-based decomposition techniques for support vector machines
    • DOI 10.1080/10556780500140714
    • T. SERAFINI AND L. ZANNI, On the working set selection in gradient-based decomposition techniques for support vector machines, Optim. Methods Softw., 20 (2005), pp. 583-596. (Pubitemid 41602158)
    • (2005) Optimization Methods and Software , vol.20 , Issue.4-5 , pp. 583-596
    • Serafini, T.1    Zanni, L.2
  • 63
    • 77956736675 scopus 로고    scopus 로고
    • A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training
    • DOI 10.1007/s10589-008-9215-4
    • P. TSENG AND S. YUN, A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training, Comput. Optim. Appl., (2008), DOI 10.1007/s10589-008-9215-4.
    • (2008) Comput. Optim. Appl.
    • Tseng, P.1    Yun, S.2
  • 66
    • 79956159699 scopus 로고    scopus 로고
    • Exploiting separability in large-scale linear support vector machine training
    • DOI 10.1007/s10589-009-9296-8
    • K. WOODSEND AND J. GONDZIO, Exploiting separability in large-scale linear support vector machine training, Comput. Optim. Appl., (2009), DOI 10.1007/s10589-009-9296-8.
    • (2009) Comput. Optim. Appl.
    • Woodsend, K.1    Gondzio, J.2
  • 67
    • 33645025197 scopus 로고    scopus 로고
    • An improved gradient projection-based decomposition technique for support vector machines
    • DOI 10.1007/s10287-005-0004-6
    • L. ZANNI, An improved gradient projection-based decomposition technique for support vector machines, Comput. Manag. Sci., 3 (2006), pp. 131-145. (Pubitemid 43414563)
    • (2006) Computational Management Science , vol.3 , Issue.2 , pp. 131-145
    • Zanni, L.1
  • 68
    • 33745784205 scopus 로고    scopus 로고
    • Parallel software for training large scale support vector machines on multiprocessor systems
    • L. ZANNI, T. SERAFINI, AND G. ZANGHIRATI, Parallel software for training large scale support vector machines on multiprocessor systems, J. Mach. Learn. Res., 7 (2006), pp. 1467-1492. (Pubitemid 44024592)
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 1467-1492
    • Zanni, L.1    Serafini, T.2    Zanghirati, G.3


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