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  • Articles: DFG German National Licenses  (3)
  • interval arithmetic  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Constructing large feasible suboptimal intervals for constrained nonlinear optimization (1995)
    Springer
    Annals of operations research 58 (1995), S. 279-293 
    Details
    ISSN: 1572-9338
    Keywords: Constrained nonlinear optimization ; sensitivity analysis ; inclusion function ; interval arithmetic ; 90C30 ; 65K05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An algorithm for finding a large feasiblen-dimensional interval for constrained global optimization is presented. Then-dimensional interval is iteratively enlarged about a seed point while maintaining feasibility. An interval subdivision method may be used to check feasibility of the growing box. The resultant feasible interval is constrained to lie within a given level set, thus ensuring it is close to the optimum. The ability to determine such a feasible interval is useful for exploring the neighbourhood of the optimum, and can be practically used in manufacturing considerations. The numerical properties of the algorithm are tested and demonstrated by an example problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096403
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Interval method for bounding level sets: Revisited and tested with global optimization problems (1990)
    Springer
    BIT 30 (1990), S. 650-657 
    Details
    ISSN: 1572-9125
    Keywords: 90C30 ; 65K05 ; Inclusion function ; interval arithmetic ; level set ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An interval method for bounding level sets, modified to increase its efficiency and to get sharper bounding boxes, is presented. The new algorithm was tested with standard global optimization test problems. The test results show that, while the modified method gives a more valuable, guaranteed reliability result set, it is competitive with non-interval methods in terms of CPU time and number of function evaluations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933213
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the selection of subdivision directions in interval branch-and-bound methods for global optimization (1995)
    Springer
    Journal of global optimization 7 (1995), S. 183-207 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; interval arithmetic ; branch-and-bound ; interval subdivision
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper investigates the influence of the interval subdivision selection rule on the convergence of interval branch-and-bound algorithms for global optimization. For the class of rules that allows convergence, we study the effects of the rules on a model algorithm with special list ordering. Four different rules are investigated in theory and in practice. A wide spectrum of test problems is used for numerical tests indicating that there are substantial differences between the rules with respect to the required CPU time, the number of function and derivative evaluations, and the necessary storage space. Two rules can provide considerable improvements in efficiency for our model algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01097060
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    Paper (German National Licenses)
    Fulltext
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