ISSN:
1573-2916
Keywords:
Branch and bound principle
;
inclusion function
;
interval extensions
;
midpoint test
;
global optimization
;
order of an interval extension
;
nonconvex optimization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider branch and bound methods for enclosing all unconstrained global minimizers of a nonconvex nonlinear twice-continuously differentiable objective function. In particular, we consider bounds obtained with interval arithmetic, with the “midpoint test,” but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undesirable cluster of boxes around each minimizer. In a previous paper, we analyzed this problem for univariate objective functions. In this paper, we generalize that analysis to multi-dimensional objective functions. As in the univariate case, the results show that the problem is highly related to the behavior of the objective function near the global minimizers and to the order of the corresponding interval extension.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01096455
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