ISSN:
1573-2878
Keywords:
Multimodal functions
;
multistage allocation
;
source of multimodality
;
discrimination of stationary points
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Multiple optimum solutions of a multistage allocation problem, well-known to chemical engineers, are analyzed. The number of local optima becomes greater with a decrease in the initial-condition value of the first stage or with an increase in the total stage number. The fact that this behavior is closely related to the flat portion of the profile of a curvef(x), which determines the objective function, is revealed. A construction method by Aris is used to give an excellent insight into this behavior. Moreover, the construction curves ensure that all stationary points are found. Finally, a theorem to discriminate local optima from stationary points, without evaluating second-order derivatives, is presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933253
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