Abstract
The linear feasibility problem arises in several areas of applied mathematics and medical science, in several forms of image reconstruction problems. The surrogate constraint algorithm of Yang and Murty for the linear feasibility problem is implemented and analyzed. The sequential approach considers projections one at a time. In the parallel approach, several projections are made simultaneously and their convex combination is taken to be used at the next iteration. The sequential method is compared with the parallel method for varied numbers of processors. Two improvement schemes for the parallel method are proposed and tested.
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The authors are indebted to K. Madsen for providing financial support to this project.
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Censor, Y., Lent, A.: Cyclic Subgradient Projections. Mathematical Programming, 24:233–235, 1982.
Censor, Y., Zenios, S. A.: Parallel Optimization: Theory, Algorithms and Applications (to be published by Oxford University Press). October 18, 1995.
García Palomares, U. M.: Parallel Projected Aggregation Methods for Solving the Convex Feasibility Problem. SIAM Journal on Optimization, 3–4:882–900, November 1993.
García Palomares, U. M., González Castaño, F. J.: Acceleration technique for solving convex (linear) systems via projection methods. Technical Report OP960614, Universidade de Vigo, ESCOLA TÉCNICA SUPERIOR DE ENXEÑEIROS DE TELECOMUNICACIÓN, Lagoas Marcosende 36200 Vigo, Espana, 1996.
Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R., Sunderam, V.: PVM: Parallel Virtual Machine. A User's Guide and Tutorial for Networked Parallel Computing. The MIT Press., Cambridge, Massachusetts, 1994.
Hiriart-Urruty, Jean-Baptiste and Lemaréchal, Claude: Convex Analysis and Minimization Algorithms. Springer-Verlag, Berlin, 1993.
Pissanetzky, Sergio: Sparse Matrix Technology. Academic Press Inc., London, 1984.
Ross, Sheldon M.: Stochastic Processes. John Wiley & Sons Inc., 1983.
Yang, K., Murty, K.G.: New Iterative Methods for Linear Inequalities. Journal of Optimization Theory and Applications, 72:163–185, January 1992.
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© 1996 Springer-Verlag Berlin Heidelberg
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Özaktaş, H., Akgül, M., Pinar, M.Ç. (1996). The parallel surrogate constraint approach to the linear feasibility problem. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_61
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DOI: https://doi.org/10.1007/3-540-62095-8_61
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