Abstract
Two examples of global optimization of multimodal functions are considered. The first problem is maximization of throughput of a network working under finite population slotted ALOHA protocol. It is assumed that the traffic load is given and each of n nodes may have its own transmission probability. The analytical solution is obtained including the results of Abramson [2] as special case. The second example is the multidimensional scaling (MDS), a well known technique for visualization and analysis of multidimensional data. The most important part of implementation of MDS is minimization of STRESS function which expresses a measure of difference between set of patterns and set of images. Analysis of local optimality conditions, presented in this paper, implies the reformulation of the problem which enables the local minimization of STRESS with quadratic rate of convergence, improving the efficiency of the corresponding MDS algorithm. Two presented problems demonstrate the examples of efficient application of local techniques based on thoroughful analytical investigation of a problem versus its solving by means of a general global optimization algorithm.
The research was partly supported by Deutsche Forschungs Gemainschaft, Danish Natural Science Research Council and Lithuanian Fund of Studies and Research
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Žilinskas, A. (2001). Two Examples of Global Optimization by Means of Local Techniques. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) From Local to Global Optimization. Nonconvex Optimization and Its Applications, vol 53. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5284-7_4
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DOI: https://doi.org/10.1007/978-1-4757-5284-7_4
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