An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms
The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate xk+1 by projecting the current point xk onto a separating hyperplane generated by a given linear combination of the original hyperplanes or half-spaces. In [12] we introduced...
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| Otros Autores: | , , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Springer Netherlands
2004
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| Sumario: | The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate xk+1 by projecting the current point xk onto a separating hyperplane generated by a given linear combination of the original hyperplanes or half-spaces. In [12] we introduced acceleration schemes for solving systems of linear equations by applying optimization techniques to the problem of finding the optimal combination of the hyperplanes within a PAM like framework. In this paper we generalize those results, introducing a new accelerated iterative method for solving systems of linear inequalities, together with the corresponding theoretical convergence results. In order to test its efficiency, numerical results obtained applying the new acceleration scheme to two algorithms introduced by García-Palomares and González- Castaño [6] are given. |
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| Bibliografía: | Bramley, R., Sameh, A., Row projection methods for large nonsymmetric linear systems (1992) SIAM J. Sci. Statist. Comput., 13, pp. 168-193 Censor, Y., Parallel application of block-iterative methods in medical imaging and radiation therapy (1988) Math. Programming, 42, pp. 307-325 Censor, Y., Zenios, S., (1997) Parallel Optimization: Theory and Applications, , Oxford Univ. Press, New York Cimmino, G., Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ric. Sci., 16, pp. 326-333 García-Palomares, U.M., Parallel projected aggregation methods for solving the convex feasibility problem (1993) SIAM J. Optim., 3, pp. 882-900 García-Palomares, U.M., González-Castaño, F.J., Incomplete projection algorithms for solving the convex feasibility problem (1998) Numer. Algorithms, 18, pp. 177-193 Gubin, L.G., Polyak, B.T., Raik, E.V., The method of projections for finding the common point of convex sets (1967) USSR Comput. Math. Math.Phys., 7, pp. 1-24 Herman, G.T., Meyer, L.B., Algebraic reconstruction techniques can be made computationally efficient (1993) IEEE Trans. Medical Imaging, 12, pp. 600-609 Saad, Y., SPARSKIT: A basic tool kit for sparse matrix computations (1990) Technical Report 90-20, , Research Institute for Avanced Computer Science. NASA Ames Research Center, Moffet Field, CA Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., A class of optimized row projection methods for solving large non-symmetric linear systems (2002) Appl. Numer. Math., 41 (4), pp. 499-513 Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., Acceleration scheme for parallel projected aggregation methods for solving large linear systems (2002) Ann. Oper. Res., 117 (1-4), pp. 95-115 Scolnik, H.D., Echebest, N., Guardarucci, M.T., Vacchino, M.C., New optimized and accelerated PAM methods for solving large non-symmetric linear systems: Theory and practice (2001) Inherently Parallel Algorithms in Feasibility and Optimization and their Applications, 8. , eds. D. Butnariu, Y. Censor and S. Reich, Studies in Computational Mathematics (Elsevier Science, Amsterdam |
| ISSN: | 10171398 |
| DOI: | 10.1023/B:NUMA.0000021777.31773.c3 |