New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds

Mathematical Programming

Volumn 106, Issue 3, 2006, Pages 403-421

  Dai, Yu Hong ^a   Fletcher, Roger ^b  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; INTERPOLATION; NUMERICAL ANALYSIS; VECTORS;

GRADIENT ALGORITHM; LINEARLY CONSTRAINED QUADRATIC PROGRAMS; NON-MONOTONE LINE SEARCH CRITERION; SECANT APPROXIMATION;

QUADRATIC PROGRAMMING;

EID: 33644511085     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-005-0595-2     Document Type: Article

References (26)

1. Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141-148 (1988)
2. Birgin, E.G., Martínez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10, 1196-1211 (2000)
3. Birgin, E.G., Martínez, J.M., Raydan, M.: Inexact spectral projected gradient methods on convex sets. IMA J. Numer. Anal. 23, 539-559 (2003)
4. Brucker, P.: An O(n) algorithm for quadratic knapsack problems. Oper. Res. Lett. 3, 163-166 (1984)
5. Calamai, P.H., Moré, J.J.: Quasi-Newton updates with bounds. SIAM J. Numer. Anal. 24, 1434-1441 (1987)
6. Dai, Y.H., Fletcher, R.: On the asymptotic behaviour of some new gradient methods, Research report NA/212, Department of Mathematics, University of Dundee, 2003, and in Mathematical Programming, Series A, Vol. 103, No. 3, 541-560 (2005)
7. Dai, Y.H., Fletcher, R.: Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming, Research report NA/215, Department of Mathematics, University of Dundee, 2003, and in Numerische Mathematik A, Vol. 100, No. 1, 21-47 (2005)
8. Dai, Y.H., Zhang, H.C.: An adaptive two-point stepsize gradient algorithm. Numer. Algorithms 27, 377-385 (2001)
9. Dolan, E.D., Moré, J.: Benchmarking optimization software with performance profiles. Math. Program. Ser. A 91, 201-203 (2002)
10. Fletcher, R.: On the Barzilai-Borwein method, Research report, Department of Mathematics, University of Dundee, 2001. and in Optimization and Control with Applications, Eds. L. Qi, K. Teo and X. Yang, Kluwer Academic Publishers, Series in Applied Optimization, (to appear).
11. Friedlander, A., Martínez, J.M., Molina, B., Raydan, M.: Gradient method with retards and generalizations. SIAM J. Numer. Anal. 36, 275-289 (1999)
12. Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton's method. SIAM J. Numer. Anal. 23, 707-716 (1986)
13. Held, M., Wolfe, P., Crowder, H.: Validation of subgradient algorithms. Math. Prog. 6, 62-88 (1974)
14. Helgason, R., Kennington, J., Lall, H.: A polynomially bound algorithms for a singly constrained quadratic program. Math. Prog. 18, 338-343 (1980)
15. Joachims, T.: Making large-scale SVM learning practical. In: Schölkopf, B., Burges, C.J.C., Smola, A. (eds.) Advances in Kernel Methods - Support Vector Learning, MIT Press, Cambridge, Massachussets, 1998
16. Meyer, R.R.: Multipoint methods for separable nonlinear networks. Math. Programming Study 22, 185-205 (1984)
17. Moré, J., Toraldo, G.: Algorithms for bound constrained quadratic programming problems. Numer. Math. 55, 377-400 (1989)
18. Pardalos, P.M., Kovoor, N.: An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds. Math. Prog. 46, 321-328 (1990)
19. Pardalos, P.M., Rosen, J.B.: Constrained global optimization: Algorithms and applications. In: Lecture Notes in Computer Science, Vol. 268 (Springer, Berlin, 1987)
20. Platt, J.C.: Fast training of support vector machines using sequential minimal optimization. In: Advances in Kernel Methods - Support Vector Learning, Schölkopf, B., Burges, C., Smola, A. (eds.) MIT Press, Cambridge, Massachusets, 1998
21. Raydan, M.: On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13, 321-326 (1993)
22. Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7, 26-33 (1997)
23. Serafini, T., Zanghirati, G., Zanni, L.: Gradient projection methods for quadratic programs and applications in training support vector machines. Research report, 2003 Optim. Meth. Software, Vol. 20, 347-372 (2005)
24. Toint, Ph.L.: A non-monotone trust region algorithm for nonlinear optimization subject to convex constraints. Math. Prog. 77, 69-94 (1997)
25. Vapnik, V.: Estimation of dependences based on empirical data. Springer-Verlag, 1982
26. Zanni, L.: An improved gradient projection-based decomposition technique for support vector machines. Research report, Dipartimento di Mathematica, Università di Modena e Reggio Emilia, Italy