Spectral projected gradient method with inexact restoration for minimization with nonconvex constraints

SIAM Journal on Scientific Computing

Volumn 31, Issue 3, 2009, Pages 1628-1652

  Gomes Ruggiero, M A ^a   Martinez J M ^a   Santos, S A ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Hard spheres problems; Inexact restoration; Nonlinear programming; Spectral projected gradients

Indexed keywords

CONSTRAINED OPTIMIZATION; GRADIENT METHODS; NUMERICAL METHODS; RESTORATION;

GRADIENT DIRECTION; HARD SPHERES; HARD-SPHERE PROBLEM; INEXACT RESTORATION; MINIMISATION; NONCONVEX CONSTRAINT; NONLINEAR OPTIMIZATION PROBLEMS; PROJECTED GRADIENT; SPECTRAL PROJECTED GRADIENT; SPECTRAL PROJECTED GRADIENT METHOD;

NONLINEAR PROGRAMMING;

EID: 61849117506     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070707828     Document Type: Article

References (47)

1. R. ANDREANI, E. G. BIRGIN, J. M. MARTÍNEZ, AND J-Y. YUAN, Spectral projected gradient and variable metric methods for optimization with linear inequalities, IMA J. Numer. Anal., 25 (2005), pp. 221-252.
2. A. ANDREANI, J. M. MARTÍNEZ, AND M. L. SCHUVERDT, On the relation between constant positive linear dependence condition and quasinormality constraint qualification, J. Optim. Theory Appl., 125 (2005), pp. 473-485.
3. J. BARZILAI AND J. M. BORWEIN, Two point step size gradient method, IMA J. Numer. Anal., 8 (1988), pp. 141-148.
4. L. BELLO AND M. RAYDAN, Convex constrained optimization for the seismic reflection tomography problem, J. Appl. Geophys., 62 (2007), pp. 158-166.
5. D. P. BERTSEKAS, On the Goldstein-Levitin-Polyak gradient projection method, IEEE Trans. Automat. Control, 21 (1976), pp. 174-184.
6. D. P. BERTSEKAS, Nonlinear Programming, 2nd ed., Athena Scientific, Belmont, MA, 1999.
7. 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.
8. E. G. BIRGIN AND J. M. MARTÍNEZ, Local convergence of an inexact-restoration method and numerical experiments, J. Optim. Theory Appl., 127 (2005), pp. 229-247.
9. E. G. BIRGIN, J. M. MARTÍNEZ, AND M. RAYDAN, Nonmonotone spectral projected gradient methods on convex sets, SIAM J. Optim., 10 (2000), pp. 1196-1211.
10. E. G. BIRGIN, J. M. MARTÍNEZ, AND M. RAYDAN, Algorithm 813 : SPG - Software for convex-constrained optimization, ACM Trans. Math. Software, 27 (2001), pp. 340-349.
11. 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.
12. J. CONWAY AND N. SLOANE, Sphere Packings, Lattices, and Groups, Springer-Verlag, Berlin, 1993.
13. D. CORES AND M. LORETO, A generalized two-point ellipsoidal anisotropic ray tracing for converted waves, Optim. Eng,. 8 (2007), pp. 373-396.
14. Y. H. DAI AND R. FLETCHER, Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming, Numer. Math., 100 (2005), pp. 21-47.
15. Y. H. DAI AND R. FLETCHER, On the asymptotic behavior of some new gradient methods, Math. Program., 103 (2005), pp. 541-559.
16. Y. H. DAI, W. W. HAGER, K. SCHITTKOWSKI, AND H. C. ZHANG, The cyclic Barzilai-Borwein method for unconstrained optimization, IMA J. Numer. Anal., 26 (2006), pp. 604-627.
17. Y. H. DAI AND L. Z. LIAO, R-linear convergence of the Barzilai and Borwein gradient method, IMA J. Numer. Anal., 22 (2002), pp. 1-10.
18. G. P. DEIDDA, E. BONOMI, AND C. MANZI, Inversion of electrical conductivity data with Tikhonov regularization approach: Some considerations, Ann. Geophys., 46 (2003), pp. 549-558.
19. J. E. DENNIS AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, NJ, 1983.
20. M. A. DINIZ-EHRHARDT, M. A. GOMES- RUGGIERO, J. M. MARTÍNEZ, AND S. A. SANTOS, Augmented Lagrangian algorithms based on the spectral projected gradient for solving nonlinear programming problems, J. Optim. Theory Appl., 123 (2004), pp. 497-517.
21. A. FRIEDLANDER, J. M. MARTÍNEZ, B. MOLINA, AND M. RAYDAN, Gradient method with retards and generalizations, SIAM J. Numer. Anal., 36 (1998), pp. 275-289.
22. A. A. GOLDSTEIN, Convex programming in Hubert space, Bull. Amer. Math. Soc., 70 (1964), pp. 709-710.
23. F. A. M. GOMES, M. C. MACIEL, AND J. M. MARTÍNEZ, Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters, Math. Program., 84 (1999), pp. 161-200.
24. M. A. GOMES-RUGGIERO, J. M. MARTÍNEZ, AND S. A. SANTOS, Inexact-restoration methods with inequality constraints and Lagrangian tangent decrease, in Proceedings of the 19th International Symposium on Mathematical Programming, Book of Abstracts Mathematical Programming Society, 2006, p. 137.
25. C. C. GONZAGA, E. W. KARAS, AND M. VANTI, A globally convergent filter method for nonlinear programming, SIAM J. Optim., 14 (2004), pp. 646-669.
26. L. GRIFPO, F. LAMPARIELLO, AND S. LUCIDI, A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal., 23 (1986), pp. 707-716.
27. L. GRIPPO AND M. SCIANDRONE, Nonmonotone derivative free methods for nonlinear equations, Comput. Optim. Appl., 37 (2007), pp. 297-328
28. Z. JIANG, Applications of conditional nonlinear optimal perturbation to the study of the stability and sensitivity of the Jovian atmosphere, Adv. Atmos. Sci., 23 (2006), pp. 775-783.
29. S. KUCHERENKO, P. BELOTTI, L. LIBERTI, AND N. MACULAN, New formulations for the kissing number problem, Discrete Appl. Math., 155 (2007), pp. 1837-1841.
30. E. S. LEVITIN AND B. T. POLYAK, Constrained minimization problems, USSR Comput. Math. Math. Phys., 6 (1966), pp. 1-50.
31. J. M. MARTÍNEZ, Inexact restoration method with Lagrangian tangent decrease and new merit function for nonlinear programming, J. Optim. Theory Appl., 111 (2001), pp. 39-58.
32. J. M. MARTÍNEZ AND E. A. PILOTTA, Inexact restoration algorithms for constrained optimization, J. Optim. Theory Appl., 104 (2000), pp. 135-163.
33. J. M. MARTÍNEZ, E. A. PILOTTA, AND M. RAYDAN, Spectral gradient methods for linearly constrained optimization, J. Optim. Theory Appl., 125 (2005), pp. 629-651.
34. B. A. MURTAGH AND M. A. SAUNDERS, MINOS 5.5 User's Guide, Technical report SOL 83-20R, Stanford University, Palo Alto, CA, 1995.
35. L. QI AND Z. WEI, On the constant positive linear dependence condition and its application to SQP methods, SIAM J. Optim., 10 (2000), pp. 963-981.
36. A. RAMIREZ-PORRAS AND W. E. VARGAS- CASTRO, Transmission of visible light through oxidized copper films: Feasibility of using a spectral projected gradient method, Appl. Opt., 43 (2004), pp. 1508-1514.
37. M. RAYDAN, On the Barzilai and Borwein choice of steplength for the gradient method, IMA J. Numer. Anal., 13 (1993), pp. 321-326.
38. M. RAYDAN, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem, SIAM J. Optim., 7 (1997), pp. 26-33.
39. M. RAYDAN AND B. F. SVAITER, Relaxed steepest descent and Cauchy-Barzilai-Borwein method, Comput. Optim. Appl., 21 (2002), pp. 155-167.
40. 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. 347-372.
41. J. W. TUKEY, Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1977.
42. W. E. VARGAS, D. E. AZOFEIFA, AND N. CLARK, Retrieved optical properties of thin films on absorbing substrates from transmittance measurements by application of a spectral projected gradient method, Thin Solid Films, 425 (2003), pp. 1-8.
43. C. Y. WANG AND Q. LIU, Convergence properties of inexact projected gradient methods, Optimization, 55 (2006), pp. 301-310.
44. C. Y. WANG, Q. LIU, AND X. M. YANG, Convergence properties of nonmonotone spectral projected gradient methods, J. Comput. Appl. Math., 182 (2005), pp. 51-66.
45. Y-X. YUAN, A new stepsize for the steepest descent method, J. Comput. Math., 24 (2006), pp. 149-156.
46. N. ZEEV, O. SAVASTA, AND D. CORES, Non-monotone spectral projected gradient method applied to full waveform inversion, Geophys. Prospecting, 54 (2006), pp. 525-534.
47. L. ZHANG AND W. J. ZHOU, Spectral gradient projection method for solving nonlinear monotone equations, J. Comput. Appl. Math., 196 (2006), pp. 478-484.