On the convergence properties of the projected gradient method for convex optimization

Computational and Applied Mathematics

Volumn 22, Issue 1, 2003, Pages 37-52

  Iusem, A N ^a  

^a IMPA   (Brazil)

Author keywords

Convex optimization; Projected gradient method; Quasi Fej r convergence

Indexed keywords

GRADIENT METHODS; NUMERICAL METHODS; STEEPEST DESCENT METHOD;

CONVERGENCE PROPERTIES; CONVEX OBJECTIVES; CONVEX OPTIMISATION; OPTIMAL SOLUTIONS; PROJECTED GRADIENT METHODS; QUASI-FEJER CONVERGENCE; STEEPEST-DESCENT METHOD; STEP SIZE; STRONG CONVERGENCE; UNCONSTRAINED MINIMIZATION PROBLEM;

CONVEX OPTIMIZATION;

EID: 33144472015     PISSN: 22383603     EISSN: 18070302     Source Type: Journal    
DOI: 10.1590/s1807-03022003000100003     Document Type: Article

References (17)

1. Alber, Ya. I., Iusem, A.N. and Solodov, M.V., On the projected subgradient method for nonsmooth convex optimization in a Hilbert space, Mathematical Programming, 81 (1998), 23–37.
2. Bereznyev, V.A., Karmanov, V.G. and Tretyakov, A.A., The stabilizing properties of the gradient method, USSR Computational Mathematics and Mathematical Physics, 26 (1986), 84–85.
3. Bertsekas, D., Nonlinear Programming, Athena Scientific, Belmont (1995).
4. Birgin, E.G. and Evtushenko, Y.G., Automatic differentiation and spectral projected gradient methods for optimal control problems, Optimization Methods and Software, 10 (1998), 125–146.
5. Birgin, E.G., Martínez, J.M. and Raydan, M., Nonmonotone spectral projected gradient methods on convex sets, SIAM Journal on Control and Optimization, 10 (2000), 1196–1211.
6. Birgin, E.G., Martínez, J.M. and Raydan, M., SPG: software for convex constrained optimization (to be published in ACM Transactions on Mathematical Software).
7. Burachik, R., Graña Drummond, L.M., Iusem, A.N. and Svaiter, B.F., Full convergence of the steepest descent method with inexact line searches, Optimization, 32 (1995), 137–146.
8. Correa, R. and Lemaréchal, C., Convergence of some algorithms for convex minimization, Mathematical Programming, 62 (1993), 261–275.
9. Gafni, E.N. and Bertsekas, D., Convergence of a gradient projection method, Technical Report LIDS-P-1201, Laboratory for Information and Decision Systems, M.I.T. (1982).
10. Golstein, E. and Tretyakov, N., Modified Lagrange Functions. Moscow (1989).
11. Hiriart Urruty, J.-B. and Lemaréchal, C., Convex Analysis and Minimization Algorithms, Springer, Berlin (1993).
12. Iusem, A.N. and Svaiter, B.F., A proximal regularization of the steepest descent method, RAIRO, Recherche Opérationelle, 29, 2, (1995), 123–130.
13. Kiwiel, K. and Murty, K.G., Convergence of the steepest descent method for minimizing quasi convex functions, Journal of Optimization Theory and Applications, 89 (1996), 221–226.
14. Nesterov, Y.E., Effective Methods in Nonlinear Programming, Moscow (1989).
15. Polyak, B.T., Introduction to Optimization, Optimization Software, NewYork (1987).
16. Svaiter, B.F., Projected gradient with Armijo search. Unpublished manuscript.
17. Zangwill, W.I., Nonlinear Programming: a Unified Approach, Prentice Hall, New Jersey (1969).