METHOD AND APPARATUS FOR
OPTIMIZING SYSTEM OPERATIONAL
PARAMETERS THROUGH AFFINE
 Inventors: Narendra K. Karmarkar, North
Plaintfield; Jeffrey C. Lagarias,
Summit, both of N.J.
 Assignee: AT&T Bell Laboratories, Murray Hill, N.J.
 Appl. No.: 899,046
 Filed: Aug. 22, 1986
 Int. Q.* G06F 15/20
 U.S. CI 364/148; 364/402
 Field of Search 364/148, 402
 References Cited
-U.S. PATENT DOCUMENTS
4.744.026 5/1988 Vanderbei 364/402
4.744.027 5/1988 Bayer et al 364/402
4.744.028 5/1988 Kamarkar 364/402
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. Kha
chiyan, 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..
Primary Examiner—Allen MacDonald
Attorney, Agent, or Firm—Henry T. Brendzel
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, xo to a next state xi 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 xi, xj, x„ .... 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.
14 Claims, 9 Drawing Sheets