| Journal: | Computational & applied mathematics |
| Database: | PERIÓDICA |
| System number: | 000310628 |
| ISSN: | 0101-8205 |
| Authors: | Iusem, A. N1 |
| Institutions: | 1Instituto de Matematica Pura e Aplicada, Rio de Janeiro. Brasil |
| Year: | 2003 |
| Volumen: | 22 |
| Number: | 1 |
| Pages: | 37-52 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Experimental, aplicado |
| English abstract | When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the noncovex case: the whole sequence converges to an optimal solution under the only hypothesis of existence of minimizers (i.e. without assuming e.g. boundedness of the level sets). In this paper we look at the projected gradient method for constrained convex minimization. Convergence of the whole sequence to a minimizer assuming only existence of solutions has also been already established for the variant in which the stepsizes are exogenously given and square summable. In this paper, we prove the result for the more standard (and also more efficient) variant, namely the one in which the stepsizes are determined through an Armijo search |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas aplicadas, Método de gradiente proyectado, Optimización convexa, Convergencia cuasi-Fejér |
| Keyword: | Mathematics, Applied mathematics, Projected gradient method, Convex optimization, Quasi-Fejér convergence |
| Full text: | Texto completo (Ver HTML) |
