8 resultados para Stochastic Approximation Algorithms

em Bulgarian Digital Mathematics Library at IMI-BAS


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2000 Mathematics Subject Classification: 62G07, 62L20.

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Various combinatorial problems are effectively modelled in terms of (0,1) matrices. Origins are coming from n-cube geometry, hypergraph theory, inverse tomography problems, or directly from different models of application problems. Basically these problems are NP-complete. The paper considers a set of such problems and introduces approximation algorithms for their solutions applying Lagragean relaxation and related set of techniques.

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2000 Mathematics Subject Classification: 62J05, 62G35

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Partial support of the Hungarian State Eötvös Scholarship, the Hungarian National Science Fund (Grant No. OTKA 42559 and 42706) and the Mobile Innovation Center, Hungary is gratefully acknowledged.

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Accelerated probabilistic modeling algorithms, presenting stochastic local search (SLS) technique, are considered. General algorithm scheme and specific combinatorial optimization method, using “golden section” rule (GS-method), are given. Convergence rates using Markov chains are received. An overview of current combinatorial optimization techniques is presented.

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*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003

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Fermentation processes as objects of modelling and high-quality control are characterized with interdependence and time-varying of process variables that lead to non-linear models with a very complex structure. This is why the conventional optimization methods cannot lead to a satisfied solution. As an alternative, genetic algorithms, like the stochastic global optimization method, can be applied to overcome these limitations. The application of genetic algorithms is a precondition for robustness and reaching of a global minimum that makes them eligible and more workable for parameter identification of fermentation models. Different types of genetic algorithms, namely simple, modified and multi-population ones, have been applied and compared for estimation of nonlinear dynamic model parameters of fed-batch cultivation of S. cerevisiae.

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2002 Mathematics Subject Classification: 65C05