Method and apparatus for optimizing system operational parameter

Details Method and apparatus for optimizing system operational parameter Method and apparatus for optimizing system operational parameter

1986-08-22

1990-04-03

MacDonald, Allen

Boots, shoes, and leggings

364402, G06F 1520

Patent

active

049145630

ABSTRACT:
Method and apparatus for optimizing the operational state of a system employing iterative steps that approximately follow a projective scaling trajectory or an affine scaling trajectory, or curve, in computing from its present state, x.sub.0 to a next state x.sub.1 toward the optimum state. The movement is made in a transformed space where the present (transformed) state of the system is at the center of the space, and the curve approximation is in the form of a power series in the step size. The process thus develops a sequence of tentative states x.sub.1, x.sub.2, x.sub.n . . . . It halts when a selected suitable stopping criterion is satisfied, and assigns the most recent tentative state as the optimized operating state of the system.

REFERENCES:
patent: 4744026 (1988-05-01), Vanderbei
patent: 4744027 (1988-05-01), Bayer et al.
patent: 4744028 (1988-05-01), Kamarkar
Linear Programming and Extensions, G. B. Danzig, 1963, Princeton University Press, Princeton, N.J., pp. 156-166.
"A Polynomial Algorithm in Linear Programming", Doklady Akademiia Nauk SSSR, 224:S, L. G. Khachiyan, 1979 (translated in 20 Soviet Mathematics Doklady 1, pp. 191-194, 1979).
"The Ellipsoid Method: A Survey", Operations Research, vol. 29, No. 6, R. G. Bland et al., 1981, pp. 1039-1091.
"A New Polynomial-Time Algorithm for Linear Programming", Proceedings of the ACM Symp. on Theory of Computer, N. K. Karmarkar, Apr. 30, 1984, pp. 302-311.
"The Ellipsoid Method and Its Consequences in Combinatorial Optimization", Combinatorica 1(2), Grotschel et al., 1981, pp. 169-197.

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