ISSN:
1572-9036
Schlagwort(e):
49M99
;
58F13
;
90B50
;
Golden Section
;
Fibonacci
;
optimization
;
dynamic process
;
chaos
;
fractal
;
Lyapunov
;
exponent
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract Certain search algorithms produce a sequence of decreasing regions converging to a pointx *. After renormalizing to a standard region at each iteration, the renormalized location ofx *, sayx x, may obey a dynamic process. In this case, simple ergodic theory might be used to compute asymptotic rates. The family of ‘second-order’ line search algorithms which contains the Golden Section (GS) method have this property. The paper exhibits several alternatives to GS which have better almost sure ergodic rates of convergence for symmetric functions despite the fact that GS is asymptotically minimax. The discussion in the last section includes weakening of the symmetry conditions and announces a backtracking bifurcation algorithm with optimum asymptotic rate.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00998150
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