Trace-and-track method

Details Trace-and-track method Trace-and-track method

1995-03-02

1997-07-22

Gordon, Paul P.

Boots, shoes, and leggings

364164, 364165, G05B 1302

Patent

active

056509260

ABSTRACT:
After an initializing step S302, a new minimum functional value F(*X.sub.2) is obtained from a present minimum functional value F(*X.sub.1) by a exploration in a step S303. F(*X.sub.1) and F(*X.sub.2) are compared in a step S304. If F(*X.sub.2).gtoreq.F(*X.sub.1), then a step size is updated in a step S999, and the step S303 and the following steps are repeated. If F(*X.sub.2)<F(*X.sub.1), then *X.sub.2 is updated as *X.sub.1, and *X.sub.1 is updated as *X.sub.0 in a step S305. F(*X.sub.1) is compared with a first functional threshold value .epsilon..sub.1 in a step S306. If F(*X.sub.1)<.epsilon..sub.1, then the process is ended in a step S318. If F(*X.sub.1).gtoreq..epsilon..sub.1, then new F(*X.sub.2) is determined according to a pattern move in a step S307. F(*X.sub.1) and F(*X.sub.2) are compared in a step S308. If F(*X.sub.2).gtoreq.F(*X.sub.1), then the step S303 and the following steps are repeated. If F(*X.sub.2)<F(*X.sub.1), then a new minimum functional value candidate F(*X.sub.3) is obtained from F(*X.sub.2) by the exploration in a step S309. F(*X.sub.2) and F(*X.sub.3) are compared in a step S310. If F(*X.sub.3)<F(*X.sub.2), then *X.sub.3 is updated as *X.sub.2 in a step S311, and the step S305 and the following steps are repeated. If F(*X.sub.3).gtoreq.F(*X.sub.2), then the step S305 and the following steps are repeated. In this manner, the convergence rate of a trace-and-track method is raised for decreasing functional value variations.

REFERENCES:
patent: 5119287 (1992-06-01), Nakamura et al.
patent: 5379210 (1995-01-01), Gruji et al.
patent: 5442510 (1995-08-01), Schwartz et al.
patent: 5495408 (1996-02-01), Caldwell
R. Hooke et al., "Direct Search Solution of Numerical and Statistical Problems", Journal of the Association for Computing Machinery, vol. 8, Apr. 1961, pp. 212-229.

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