A non-monotonic method for large-scale non-negative least squares

Optimization Methods and Software

Volumn 28, Issue 5, 2013, Pages 1012-1039

  Kim, Dongmin ^a   Sra, Suvrit ^b   Dhillon, Inderjit S ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Barzilai Borwein stepsize; gradient projection method; large scale; least squares; NNLS; non monotonic descent; nonnegativity constraints

Indexed keywords

GRADIENT PROJECTION METHODS; LARGE-SCALE; LEAST SQUARE; NNLS; NON-MONOTONIC DESCENT; NON-NEGATIVITY CONSTRAINTS; STEP SIZE;

ALGORITHMS; GRADIENT METHODS;

LEAST SQUARES APPROXIMATIONS;

EID: 84882316285     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2012.656368     Document Type: Article

References (31)

1. Barzilai, J., and, Borwein, J. M. 1988. Two-point step size gradient methods. IMA J. Numer. Anal., 8: 141-148.
2. Ben-Tal, A., and, Nemirovski, A. 2005. Non-euclidean restricted memory level method for large-scale convex optimization. Math. Progr. A, 102: 407-456. (Pubitemid 40536649)
3. Bertsekas, D. P. 1999. Nonlinear Programming, 2, MA: Athena Scientific.
4. Bierlaire, M., Toint, P. L., and, Tuyttens, D. 1991. On iterative algorithms for linear least squares problems with bound constraints. Linear Algebra Appl., 143: 111-143.
5. Birgin, E. G., Martínez, J. M., and, Raydan, M. 2000. Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim., 10: 1196-1211.
6. Birgin, E. G., Martínez, J. M., and, Raydan, M. 2001. Algorithm 813: SPG-Software for Convex-constrained Optimization. ACM Trans. Math. Softw., 27: 340-349. (Pubitemid 33654982)
7. Birgin, E. G., Martínez, J. M., and, Raydan, M. 2002. Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl., 23: 101-125. (Pubitemid 35167001)
8. Birgin, E. G., Martínez, J. M., and, Raydan, M. 2003. Inexact spectral projected gradient methods on convex sets. IMA J. Numer. Anal., 23: 539-559. (Pubitemid 37445929)
9. Björck, A. 1996. Numerical Methods for Least Squares Problems, Philadelphia, PA: SIAM.
10. Bro, R., and, Jong, S. D. 1997. A fast non-negativity-constrained least squares algorithm. J. Chemometrics, 11: 393-401. (Pubitemid 127478570)
11. Burke, J. V., and, Moré, J. J. 1988. On the identification of active constraints. SIAM J. Numer. Anal., 25: 1197-1211.
12. Byrd, R., Lu, P., Nocedal, J., and, Zhu, C. 1995. A limited memory algorithm for bound constrained optimization. SIAM J. Scient. Comput., 16: 1190-1208.
13. Cruz, W. L., and, Raydan, M. 2003. Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Meth. Softw., 18: 583-599.
14. Dai, Y. H., and, Fletcher, R. 2005. Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming. Numerische Mathematik, 100: 21-47. (Pubitemid 40405555)
15. Friedlander, A., Martínez, J. M., and, Raydan, M. 1995. A new method for large-scale box constrained convex quadratic minimization problems. Optim. Meth. Softw., 5: 55-74.
16. Gill, P. E., Murray, W., and, Wright, M. H. 1981. Practical Optimization, New York, NY: Academic Press.
17. Grippo, L., and, Sciandrone, M. 2002. Nonmonotone globalization techniques for the Barzilai-Borwein gradient method. Comput. Optim. Appl., 23: 143-169. (Pubitemid 35377442)
18. Hager, W. W., and, Zhang, H. 2006. A new active set algorithm for box constrained optimization. SIAM J. Optim., 17: 526-557. (Pubitemid 46798079)
19. Hirsch, M., Sra, S., Schölkopf, B., and, Harmeling, S. 2010. Efficient filter flow for space-variant multiframe blind deconvolution. CVPR,. June
20. Kim, D., Sra, S., and, Dhillon, I. S. 2007. Fast newton-type methods for the least squares nonnegative matrix approximation problem. SIAM DM
21. Lawson, C. L., and, Hanson, R. J. 1974. Solving Least Squares Problems, Englewood Cliffs, NJ: Prentice-Hall.
22. Lin, C. J., and, Moré, J. J. 1999. Newton's method for large bound-constrained optimization problems. SIAM J. Optim., 9: 1100-1127. (Pubitemid 129489319)
23. Moré, J. J., and, Toraldo, G. 1991. On the solution of large quadratic programming problems with bound constraints. SIAM J. Optim., 1: 93-113.
24. Nagy, J., and, Strakos, Z. 2000. Enforcing nonnegativity in image reconstruction algorithms. Math. Model. Estimation Imag., 4121: 182-190.
25. Nemirovski, A., Juditsky, A., Land, G., and, Shapiro, A. 2009. Robust stochastic approximation approach to stochastic programming. SIAM J. Optim., 19: 1574-1609.
26. Nocedal, J., and, Wright, S. 2006. Numerical Optimization, 2, Berlin: Springer.
27. Raydan, M. 1993. On the Barzilai and Borwein choice of the steplength for the gradient method. IMA J. Numer. Anal., 13: 321-326.
28. Reader, A. J., and, Zaidi, H. 2007. Advances in PET image reconstruction. PET Clin., 2: 173-190.
29. Rosen, J. B. 1960. The gradient projection method for nonlinear programming. part I. linear constraints. J. SIAM, 8: 181-217.
30. Schittkowski, K. 1983. The numerical solution of constrained linear least-squares problems. IMA J. Numer. Anal., 3: 11-36.
31. Vo, N., Moran, B., and, Challa, S. 2009. Nonnegative-least-square classifier for face recognition. Adv. Neural Networks-ISNN, 2009: 449-456.