Data processing systems and methods for linear programming

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364841, 364822, 364845, 364837, G06G 700

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051857154

ABSTRACT:
Data processing systems are described for processing linear programming problems. The invention employs optical (100) or digital (150) processors to perform Gaussian pivot operations by performing outer product matrix operations in parallel. The present invention can solve linear programming problems utilizing various techniques, including the Simplex and Karmarkar algorithms. This results in a greatly improved speed in solving linear programs over prior techniques involving sequential computing.

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patent: 4744027 (1988-05-01), Bayer et al.
patent: 4744028 (1988-05-01), Karmarkar
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patent: 4843587 (1989-06-01), Schlunt et al.
patent: 4914563 (1990-04-01), Karmarkar et al.
Proceedings of the 1988 International Conference on Parallel Processing, Aug. 15-19, 1988, vol. III Algorithms and Applications, pp. 264-271, The Pennsylvania State University Press, University Park, U.S., C. B. Stunkel.
R. A. Athale and W. C. Collins, "Optical matrix Multiplier Based on Outer Product Decomposition", Applied Optics, 21, pp. 2089 (1982).
Sotter et al., "Programmable Real Time Incoherent Matrix Multiplier for Optical Processing", Applied Optics, 25, pp. 2295-2305 (1906).
V. N. Faddeeva, Computational Method of Linear Algebra, Dover Publications, New York, N.Y. (1959).
K. G. Murty, Linear Complementarity Problem, Linear and Nonlinear Programming, Heldermann Verlag, Berlin, 1988.

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